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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
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
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 …
Collapse For The Higher-Order Nonlinear Schrödinger Equation, V. Achilleos, S. Diamantidis, D. J. Frantzeskakis, T. P. Horikis, N. I. Karachalios, P. G. Kevrekidis
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 …
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
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 …
Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena
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 …
Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed
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 …
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Mathematics and Statistics Department Faculty Publication Series
We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals “negative mass” regimes, where corresponding “negative mass” bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity …
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
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
Mathematics and Statistics Department Faculty Publication Series
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 …
Lattice Three Dimensional Skyrmions Revisited, E. G. Charalampidis, T. A. I, P. G. Kevrekidis
Lattice Three Dimensional Skyrmions Revisited, E. G. Charalampidis, T. A. I, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, an a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the three dimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed: and their stability under small perturbation sis explored by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, …
Wave Patterns Generated By A Supersonic Moving Body In A Binary Bose-Einstein Condensate, Yg Gladush, Am Kamchatnov, Z Shi, Pg Kevrekidis, Dj Frantzeskakis, Ba Malomed
Wave Patterns Generated By A Supersonic Moving Body In A Binary Bose-Einstein Condensate, Yg Gladush, Am Kamchatnov, Z Shi, Pg Kevrekidis, Dj Frantzeskakis, Ba Malomed
Mathematics and Statistics Department Faculty Publication Series
Generation of wave structures by a two-dimensional (2D) object (laser beam) moving in a 2D two-component Bose-Einstein condensate with a velocity greater than the two sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called “ship waves” are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, …
Multistable Solitons In Higher-Dimensional Cubic-Quintic Nonlinear Schrodinger Lattices, C Chong, R Carretero-Gonzalez, Ba Malomed, Pg Kevrekidis
Multistable Solitons In Higher-Dimensional Cubic-Quintic Nonlinear Schrodinger Lattices, C Chong, R Carretero-Gonzalez, Ba Malomed, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete …
Interlaced Solitons And Vortices In Coupled Dnls Lattices, J Cuevas, Qe Hoq, H Susanto, Pg Kevrekidis
Interlaced Solitons And Vortices In Coupled Dnls Lattices, J Cuevas, Qe Hoq, H Susanto, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort …
Solitons In Quasi-One-Dimensional Bose-Einstein Condensates With Competing Dipolar And Local Interactions, J Cuevas, Ba Malomed, Pg Kevrekidis, Dj Frantzeskakis
Solitons In Quasi-One-Dimensional Bose-Einstein Condensates With Competing Dipolar And Local Interactions, J Cuevas, Ba Malomed, Pg Kevrekidis, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space, and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for \textit{subfundamental solitons} (SFSs) is found in the second …
Spinor Bose-Einstein Condensate Flow Past An Obstacle, As Rodrigues, Pg Kevrekidis, R Carretero-Gonzalez, Dj Frantzeskakis, P Schmelcher, Tj Alexander, Ys Kivshar
Spinor Bose-Einstein Condensate Flow Past An Obstacle, As Rodrigues, Pg Kevrekidis, R Carretero-Gonzalez, Dj Frantzeskakis, P Schmelcher, Tj Alexander, Ys Kivshar
Mathematics and Statistics Department Faculty Publication Series
We study the flow of a spinor (F=1) Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions, and find that the system demonstrates two speeds of sound that are identified analytically. Numerical simulations reveal the nucleation of macroscopic nonlinear structures, such as dark solitons and vortex-antivortex pairs, as well as vortex rings in one- and higher-dimensional settings, respectively, when a localized defect (e.g., a blue-detuned laser beam) is dragged through the spinor condensate at a speed larger than the second critical speed.
Dipole And Quadrupole Solitons In Optically-Induced Two-Dimensional Defocusing Photonic Lattices, H Susanto, Kjh Law, Pg Kevrekidis, L Tang, C Lou, X Wang, Z Chen
Dipole And Quadrupole Solitons In Optically-Induced Two-Dimensional Defocusing Photonic Lattices, H Susanto, Kjh Law, Pg Kevrekidis, L Tang, C Lou, X Wang, Z Chen
Mathematics and Statistics Department Faculty Publication Series
We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an optical lattice (OL) and/or a parabolic magnetic trap. We connect such structures with twisted localized modes (TLMs) that were previously found in the discrete nonlinear Schrödinger equation. Families of these structures are found as functions of the OL strength, tightness of the magnetic trap and chemical potential, and their stability regions are identified. Stable bound states of two TLMs are also found. In the case when the TLMs are unstable, …