Physical Sciences and Mathematics | Open Access Articles

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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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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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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Solitary Waves, Periodic And Elliptic Solutions To The Benjamin, Bona & Mahony (Bbm) Equation Modified By Viscosity, S.C. Mancas, Harihar Khanal, Shahrdad G. Sajjadi Jan 2011

Solitary Waves, Periodic And Elliptic Solutions To The Benjamin, Bona & Mahony (Bbm) Equation Modified By Viscosity, S.C. Mancas, Harihar Khanal, Shahrdad G. Sajjadi

Publications

We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time variables is included. The 2D CCQGLE is solved by a powerful Fourier spectral method, i.e., a Fourier spatial discretization and an explicit scheme for time differencing. Varying the system’s parameters, and using different initial conditions, numerical simulations reveal 2D solitons in the form of stationary, pulsating and exploding solitons which possess very distinctive properties. For certain region of parameters, we have also found stable coherent structures in the form of spinning (vortex) solitons which exist as a result …

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Numerical Simulations Of Snake Dissipative Solitons In Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, Harihar Khanal Apr 2009

Numerical Simulations Of Snake Dissipative Solitons In Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, Harihar Khanal

Publications

Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation …

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Interaction Of Tollmien-Schlichting Waves In The Air With The Sea Surface, Shahrdad G. Sajjadi, Harihar Khanal Jan 2009

Interaction Of Tollmien-Schlichting Waves In The Air With The Sea Surface, Shahrdad G. Sajjadi, Harihar Khanal

Publications

No abstract provided.

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Nonlinear Equations And Wavelets, Andrei Ludu Jan 2003

Nonlinear Equations And Wavelets, Andrei Ludu

Andrei Ludu

No abstract provided.

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Nonlinear Phenomena In Nuclei: The Antisoliton Model For Fission, Andrei Ludu Jan 1999

Nonlinear Phenomena In Nuclei: The Antisoliton Model For Fission, Andrei Ludu

Andrei Ludu

No abstract provided.

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Patterns On Liquid Surfaces: Cnoidal Waves, Compactons And Scaling, Andrei Ludu Jan 1998

Patterns On Liquid Surfaces: Cnoidal Waves, Compactons And Scaling, Andrei Ludu

Andrei Ludu

Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated. Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discussed. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one re-obtains the well-known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear …

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Alpha+28si Cluster Structure As Solitons On The Nuclear Surface, Andrei Ludu Jan 1995