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We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where…

Fluid Dynamics · Physics 2019-03-25 Yury Stepanyants

We study solitons in the two-dimensional defocusing nonlinear Schroedinger equation with the spatio-temporal modulation of the external potential. The spatial modulation is due to a square lattice; the resulting macroscopic diffraction is…

Pattern Formation and Solitons · Physics 2015-05-30 Ramon Herrero , I. V. Barashenkov , N. V. Alexeeva , Kestutis Staliunas

The nonlinear Schr\"odinger equation based on slowly varying approximation is usually applied to describe the pulse propagation in nonlinear waveguides. However, for the case of the front induced transitions (FITs), the pump effect is well…

Optics · Physics 2019-09-04 Mahmoud A. Gaafar , Hagen Renner , Alexander Y. Petrov , Manfred Eich

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically…

Pattern Formation and Solitons · Physics 2016-08-03 M. E. Lebedev , G. L. Alfimov , Boris A. Malomed

The nonlinear Schrodinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predicts the evolution of modulated…

Fluid Dynamics · Physics 2019-03-05 John D. Carter , Christopher W. Curtis , Henrik Kalisch

In the present work, we consider the existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schr\"odinger equation with both fourth and second order dispersion terms. We first give a criterion for the…

Pattern Formation and Solitons · Physics 2021-04-01 Ross Parker , Alejandro Aceves

A nonlinear Schr\"odinger equation is derived for the dynamics of a beam of ultracold fermionic atoms traversing a Bose-Einstein condensate. The condensate phonon modes are shown to provide a nonlinear medium for the fermionic atoms. A…

Statistical Mechanics · Physics 2016-08-31 Weiping Zhang , Han Pu , Chris P. Search , Pierre Meystre , E. M. Wright

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…

Pattern Formation and Solitons · Physics 2013-11-28 R. K. Jackson , R. Marangell , H. Susanto

The universal theory of weakly nonlinear wave packets given by the nonlinear Schr\"odinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple scale analysis carried out beyond all…

Pattern Formation and Solitons · Physics 2023-02-02 Gregory Kozyreff

The existence of ``dispersion-managed solitons'', i.e., stable pulsating solitary-wave solutions to the nonlinear Schr\"{o}dinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 Simon Clarke , Boris A. Malomed , Roger Grimshaw

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…

Exactly Solvable and Integrable Systems · Physics 2022-10-21 Mark J. Ablowitz , Joel B. Been , Lincoln D. Carr

The semiclassical limit of the derivative nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. The spectrum of the associated scattering problem for a certain class of initial conditions,…

Exactly Solvable and Integrable Systems · Physics 2025-12-01 Zachery Wolski , Zechuan Zhang , Gino Biondini , Gregor Kovačič

A new nonlinear model is proposed for tuneable lasers. Using the generalized nonlinear Schr\"odinger equation as a starting point, expressions for the transformations undergone by the pulse are derived for each of the five components (gain,…

Optics · Physics 2020-02-17 Brady Metherall , C. Sean Bohun

We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schr\"odinger equation. The procedures are based on simple transformations of the soliton pattern in the…

Pattern Formation and Solitons · Physics 2020-03-03 Quan M. Nguyen , Toan T. Huynh

The nonlinear Schroedinger equation with a third-order dispersive term is considered. Infinite families of embedded solitons, parameterized by the propagation velocity, are found through a gauge transformation. By applying this…

Pattern Formation and Solitons · Physics 2007-05-23 Jianke Yang , Triantaphyllos R. Akylas

It is known that a nonlinear Schr\"odinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron-positron plasmas in the weakly and strongly magnetized limits. Here, we show that such…

Plasma Physics · Physics 2023-09-13 Felipe A. Asenjo

The nonlinear Schr\"odinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of…

Optics · Physics 2008-10-30 Jonatan Lenells

Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 Jyh-Hao Lee , Oktay K. Pashaev

We carry out a group-theoretical study of the pair of nonlinear Schr\"{o}dinger equations describing the propagation of waves in nonlinear birefringent optical fibers. We exploit the symmetry algebra associated with these equations to…

Condensed Matter · Physics 2009-10-22 E. Alfinito , M. Leo , R. A. Leo , G. Soliani , L. Solombrino

The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…

Pattern Formation and Solitons · Physics 2016-09-08 John D. Carter , Harvey Segur