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Solitons

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Articles 1 - 30 of 84

Full-Text Articles in Physical Sciences and Mathematics

Interactions And Dynamics Of One-Dimensional Droplets, Bubbles And Kinks, Garyfallia Katsimiga, Simeon I. Mistakidis, Boris A. Malomed, Dimitris J. Frantzeskakis, Ricardo Carretero-Gonzalez, Panayotis G. Kevrekidis Sep 2023

Interactions And Dynamics Of One-Dimensional Droplets, Bubbles And Kinks, Garyfallia Katsimiga, Simeon I. Mistakidis, Boris A. Malomed, Dimitris J. Frantzeskakis, Ricardo Carretero-Gonzalez, Panayotis G. Kevrekidis

Physics Faculty Research & Creative Works

We Explore The Dynamics And Interactions Of Multiple Bright Droplets And Bubbles, As Well As The Interactions Of Kinks With Droplets And With Antikinks, In The Extended One-Dimensional Gross–Pitaevskii Model Including The Lee–Huang–Yang Correction. Existence Regions Are Identified For The One-Dimensional Droplets And Bubbles In Terms Of Their Chemical Potential, Verifying The Stability Of The Droplets And Exposing The Instability Of The Bubbles. The Limiting Case Of The Droplet Family Is A Stable Kink. The Interactions Between Droplets Demonstrate In-Phase (Out-Of-Phase) Attraction (Repulsion), With The So-Called Manton's Method Explicating The Observed Dynamical Response, And Mixed Behavior For Intermediate Values Of …

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Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias Apr 2023

Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias

Doctoral Dissertations

In recent years, there has been an explosion of interest in media bearing quartic
dispersion. After the experimental realization of so-called pure-quartic solitons, a
significant number of studies followed both for bright and for dark solitonic struc-
tures exploring the properties of not only quartic, but also setic, octic, decic etc.
dispersion, but also examining the competition between, e.g., quadratic and quartic
dispersion among others.
In the first chapter of this Thesis, we consider the interaction of solitary waves in
a model involving the well-known φ4 Klein-Gordon theory, bearing both Laplacian and biharmonic terms with different prefactors. As a …

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Darboux Transformation And Solitonic Solution To The Coupled Complex Short Pulse Equation, Bao-Feng Feng, Liming Ling Sep 2022

Darboux Transformation And Solitonic Solution To The Coupled Complex Short Pulse Equation, Bao-Feng Feng, Liming Ling

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright soliton, dark-soliton, breather and rogue wave solutions to the CCSP equation. In case of vanishing boundary condition (VBC), we perform the inverse scattering analysis to understand the soliton solution better. Breather and rogue wave solutions are constructed in case of non-vanishing boundary condition (NVBC). Moreover, we conduct a modulational instability (MI) analysis based on the method of squared eigenfunctions, whose result confirms the condition for the existence of rogue …

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Hamiltonian Approach To Modelling Interfacial Internal Waves Over Variable Bottom, Rossen Ivanov, Calin Martin, Michail Todorov Jan 2022

Hamiltonian Approach To Modelling Interfacial Internal Waves Over Variable Bottom, Rossen Ivanov, Calin Martin, Michail Todorov

Articles

We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave–current interactions), geophysical effects (Coriolis force) and a variable bathymetry. An example of the physical situation described above is well illustrated by the equatorial internal waves in the presence of the Equatorial Undercurrent (EUC). We find that the interface (physically coinciding with the thermocline and the pycnocline) satisfies in the long wave approximation a KdV–mKdV type equation with variable coefficients. The soliton propagation over variable depth leads to effects such as soliton …

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Coherent Control Of Dispersive Waves, Jimmie Adriazola Dec 2021

Coherent Control Of Dispersive Waves, Jimmie Adriazola

Dissertations

This dissertation addresses some of the various issues which can arise when posing and solving optimization problems constrained by dispersive physics. Considered here are four technologically relevant experiments, each having their own unique challenges and physical settings including ultra-cold quantum fluids trapped by an external field, paraxial light propagation through a gradient index of refraction, light propagation in periodic photonic crystals, and surface gravity water waves over shallow and variable seabeds. In each of these settings, the physics can be modeled by dispersive wave equations, and the technological objective is to design the external trapping fields or propagation media such …

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Soliton Based All-Optical Data Processing In Waveguides, Amaria Javed Oct 2021

Soliton Based All-Optical Data Processing In Waveguides, Amaria Javed

Dissertations

The growing demand for higher data processing speed and capacity motivates the replacement of the current electronic data processing by optical data processing in analogy with the successful replacement of electronic data communication by optical data communication. In a quest to achieve comprehensive optical data processing we aim at using solitons in waveguide arrays to perform all-optical data processing operations. Solitons are special nonlinear waves appreciated for their ability to conserve their shape and velocity before and after scattering. They are observed naturally in diverse fields of science, namely, nonlinear physics, mathematics, hydrodynamics, biophysics, and quantum field theory, etc. with …

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Nonlinear Schrödinger Equation Solitons On Quantum Droplets, A. Ludu, A.S. Carstea Jul 2021

Nonlinear Schrödinger Equation Solitons On Quantum Droplets, A. Ludu, A.S. Carstea

Publications

Irrotational flow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrödinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum, and parity for …

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Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis Jan 2021

Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor F = 1 Bose-Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark-dark-bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark-bright-bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature …

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Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose-Einstein Condensates, Garyfallia Katsimiga, Simeon I. Mistakidis, P. Schmelcher, P. G. Kevrekidis Jan 2021

Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose-Einstein Condensates, Garyfallia Katsimiga, Simeon I. Mistakidis, P. Schmelcher, P. G. Kevrekidis

Physics Faculty Research & Creative Works

We Present The Phase Diagram, The Underlying Stability And Magnetic Properties As Well As The Dynamics Of Nonlinear Solitary Wave Excitations Arising In The Distinct Phases Of A Harmonically Confined Spinor F = 1 Bose-Einstein Condensate. Particularly, It Is Found That Nonlinear Excitations In The Form Of Dark-Dark-Bright Solitons Exist In The Antiferromagnetic And In The Easy-Axis Phase Of A Spinor Gas, Being Generally Unstable In The Former While Possessing Stability Intervals In The Latter Phase. Dark-Bright-Bright Solitons Can Be Realized In The Polar And The Easy-Plane Phases As Unstable And Stable Configurations Respectively; The Latter Phase Can Also Feature …

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On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz Jan 2021

On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz

Turkish Journal of Mathematics

In this paper we study some semisymmetry conditions and some soliton types on $f$-Kenmotsu $3$-manifolds with respect to the Schouten-van Kampen connection.

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On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov Jan 2020

On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov

Articles

A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …

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Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr Jan 2020

Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr

Articles

A dressing method is applied to a matrix Lax pair for the Camassa–Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa–Holm equation are re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.

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Asymptotic And Numerical Analysis Of Coherent Structures In Nonlinear Schrodinger-Type Equations, Cory Ward Jul 2019

Asymptotic And Numerical Analysis Of Coherent Structures In Nonlinear Schrodinger-Type Equations, Cory Ward

Doctoral Dissertations

This dissertation concerns itself with coherent structures found in nonlinear Schrödinger-type equations and can be roughly split into three parts. In the first part we study a deformation of the defocusing nonlinear Schrödinger (NLS) equation, the defocusing Camassa-Holm NLS (CH-NLS) equation in both one and two space dimensions. We use asymptotic multiscale expansion methods to reduce this model to a Boussinesq-like equation, which is then subsequently used to obtain approximate solitary wave solutions for both the 1D and 2D CH-NLS equations. We then use direct numerical simulations to investigate the validity of these approximate solutions, their evolution, and their head-on …

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Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov Jan 2019

Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov

Articles

Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups GR ≃ Dh. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the GR-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with Dh symmetries are presented.

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Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov Jan 2019

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

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Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov Jan 2019

Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov

Articles

We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …

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Entanglement Entropy, Dualities, And Deconfinement In Gauge Theories, Mohamed M. Anber, Benjamin J. Kolligs Aug 2018

Entanglement Entropy, Dualities, And Deconfinement In Gauge Theories, Mohamed M. Anber, Benjamin J. Kolligs

Portland Institute for Computational Science Publications

Computing the entanglement entropy in confining gauge theories is often accompanied by puzzles and ambiguities. In this work we show that compactifying the theory on a small circle S 1/L evades these difficulties. In particular, we study Yang-Mills theory on R3×S 1/L with double-trace deformations or adjoint fermions and hold it at temperatures near the deconfinement transition. This theory is dual to a multi-component (electric-magnetic) Coulomb gas that can be mapped either to an XY-spin model with Zp symmetry-preserving perturbations or dual Sine-Gordon model. The entanglement entropy of the dual SineGordon model exhibits an extremum at the …

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Neutrino Pair Cerenkov Radiation For Tachyonic Neutrinos, Ulrich D. Jentschura, Istvan Nandori Nov 2017

Neutrino Pair Cerenkov Radiation For Tachyonic Neutrinos, Ulrich D. Jentschura, Istvan Nandori

Physics Faculty Research & Creative Works

The emission of a charged light lepton pair by a superluminal neutrino has been identified as a major factor in the energy loss of highly energetic neutrinos. The observation of PeV neutrinos by IceCube implies their stability against lepton pair Cerenkov radiation. Under the assumption of a Lorentz-violating dispersion relation for highly energetic superluminal neutrinos, one may thus constrain the Lorentz-violating parameters. A kinematically different situation arises when one assumes a Lorentz-covariant, space-like dispersion relation for hypothetical tachyonic neutrinos, as an alternative to Lorentz-violating theories. We here discuss a hitherto neglected decay process, where a highly energetic tachyonic neutrino may …

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Kinetic Theory Of Dark Solitons With Tunable Friction, Hilary M. Hurst, Dimitry K. Efimkin, I. B. Spielman, Victor Galitski May 2017

Kinetic Theory Of Dark Solitons With Tunable Friction, Hilary M. Hurst, Dimitry K. Efimkin, I. B. Spielman, Victor Galitski

Faculty Research, Scholarly, and Creative Activity

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a non-interacting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semi-classical dynamics of the dark soliton, a particle-like object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative mass …

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Global Well-Posedness For The Derivative Nonlinear Schrödinger Equation Through Inverse Scattering, Jiaqi Liu Jan 2017

Global Well-Posedness For The Derivative Nonlinear Schrödinger Equation Through Inverse Scattering, Jiaqi Liu

Theses and Dissertations--Mathematics

We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.

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Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed Sep 2016

Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed

Efstathios Charalampidis

We study a two component nonlinear Schrodinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes …

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Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis Sep 2016

Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis

Efstathios Charalampidis

In this work, we consider the dynamics of vector rogue waves and ark bright solitons in two component nonlinear Schrodinger equations with various physically motivated time dependent non linearity coefficients, as well as spatio temporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark bright boomeron like soliton solutions of the latter are converted back into ones of the original non autonomous model. Using direct numerical simulations we find that, in most cases, the rogue waves formation is rapidly followed by a modulational instability that leads …

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Resonant Solutions To (3+1)-Dimensional Bilinear Differential Equations, Yue Sun Mar 2016

Resonant Solutions To (3+1)-Dimensional Bilinear Differential Equations, Yue Sun

USF Tampa Graduate Theses and Dissertations

In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by Dp-operators with p = 5, which have resonant solutions. We construct resonant solutions by using the linear superposition principle and parameterizations of wave numbers and frequencies. We test different values of p in Maple computations, and generate three classes of generalized bilinear differential equations and their resonant solutions when p = 5.

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On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov Jan 2016

On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov

Articles

We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.

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Collapse For The Higher-Order Nonlinear Schrödinger Equation, V. Achilleos, S. Diamantidis, D. J. Frantzeskakis, T. P. Horikis, N. I. Karachalios, P. G. Kevrekidis Jan 2016

Collapse For The Higher-Order Nonlinear Schrödinger Equation, V. Achilleos, S. Diamantidis, D. J. Frantzeskakis, T. P. Horikis, N. I. Karachalios, P. G. Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schrödinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data, are …

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Two-Dimensional Structures In The Quintic Ginzburg-Landau Equation, Florent Bérard, Charles-Julien Vandamme, S.C. Mancas Aug 2015

Two-Dimensional Structures In The Quintic Ginzburg-Landau Equation, Florent Bérard, Charles-Julien Vandamme, S.C. Mancas

Publications

By using ZEUS cluster at Embry-Riddle Aeronautical University we perform extensive numerical simulations based on a two-dimensional Fourier spectral method Fourier spatial discretization and an explicit scheme for time differencing) to find the range of existence of the spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation with cubic and quintic nonlinearities. We start from the parameters used by Akhmediev et. al. and slowly vary them one by one to determine the regimes where solitons exist as stable/unstable structures. We present eight classes of dissipative solitons from which six are known (stationary, pulsating, vortex spinning, filament, exploding, creeping) and two are …

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Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, Efstathios G. Charalampidis, Christopher Chong, Eunho Kim, Heetae Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, Chiara Daraio, Jianke Yang Jan 2015

Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, Efstathios G. Charalampidis, Christopher Chong, Eunho Kim, Heetae Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, Chiara Daraio, Jianke Yang

Mathematics and Statistics Department Faculty Publication Series

This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the Nonlinear Schr¨odinger (NLS) equation predicts the corresponding modes fairly well. We propose that nonlinear multi-modal …

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Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena Jan 2015

Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena

Mathematics and Statistics Department Faculty Publication Series

In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross–Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-continuum limit of vanishing coupling). Numerous unexpected features are identified including a staggered solitary pattern emerging from a single site excitation, as well as two- and three-site excitations playing a role analogous to one- and two-site excitations, respectively, of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states …

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Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed Jan 2015

Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed

Mathematics and Statistics Department Faculty Publication Series

We study a two component nonlinear Schrodinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes …

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Pulses And Snakes In Ginzburg-Landau Equation, S.C. Mancas, Roy S. Choudhury Jan 2015

Pulses And Snakes In Ginzburg-Landau Equation, S.C. Mancas, Roy S. Choudhury

Publications

Using a variational formulation for partial differential equations combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the dependence of both their shape and stability on the physical parameters of the cubic-quintic Ginzburg–Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the CGLE …

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