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A class of non-local non-linear Schrodinger equations(NLSE) is considered in an external potential with space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization…

Exactly Solvable and Integrable Systems · Physics 2015-05-20 Debdeep Sinha , Pijush K. Ghosh

The nonlinear Schr\"odinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schr\"odinger equation as well as more exotic solutions such as solitary waves…

Quantum Gases · Physics 2024-07-08 David B. Reinhardt , Dean Lee , Wolfgang P. Schleich , Matthias Meister

We derive the two-breather solution of the class I infinitely extended nonlinear Schrodinger equation (NLSE). We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free…

Exactly Solvable and Integrable Systems · Physics 2020-09-22 Matthew Crabb , Nail Akhmediev

We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…

Mathematical Physics · Physics 2010-11-25 Erwin Suazo , Sergei K. Suslov

We consider a three spin component Bose Einstein Condensate as described by as many coupled nonlinear Schroedinger equations. For a very special ratio of the coupling constants, exact N soliton solutions to this set of equations are known.…

Quantum Gases · Physics 2014-01-28 Piotr Szankowski , Marek Trippenbach , Eryk Infeld

The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…

Condensed Matter · Physics 2009-10-31 Lincoln D. Carr , J. Nathan Kutz , William P. Reinhardt

We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…

Computational Physics · Physics 2021-12-08 Sergei Manzhos , Tucker Carrington

Existence of a new class of soliton solutions is shown for higher order nonlinear Schrodinger equation, describing thrid order dispersion, Kerr effect and stimulated Raman scattering. These new solutions have been obtaiened by invoking a…

solv-int · Physics 2007-05-23 Sasanka Ghosh , Sudipta Nandy

In this paper, we give a proof of the existence of stationary dark soliton solutions or heteroclinic orbits of nonlinear equations of Schr\"odinger type with periodic inhomogeneous nonlinearity. The result is illustrated with examples of…

Pattern Formation and Solitons · Physics 2015-05-20 J. Belmonte-Beitia , J. Cuevas

Dynamics of solitons is considered in the framework of an extended nonlinear Schrodinger equation (NLSE), which is derived from a system of the Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves. The…

Optics · Physics 2014-03-05 E. M. Gromov , B. A. Malomed

A brief review of recent research on soliton and black hole solutions of Einstein's equations with nonlinear field sources is presented and some open questions are pointed out.

General Relativity and Quantum Cosmology · Physics 2016-08-14 Piotr Bizoń

Normalized ground state solutions (NGSS) of Schrodinger equations (SE) have attracted the attention of many research groups during the last decades. This is essentially due to their relevance in many fields in physics and engineering, where…

Analysis of PDEs · Mathematics 2023-11-29 Hichem Hajaiej , Linjie Song

Extended Self-Similarity (ESS) is a widely used tool for uncovering universal power-law scaling in systems dominated by nonlinear interactions. This work demonstrates that ESS scaling can also emerge in a system governed by purely linear…

Optics · Physics 2026-01-27 Mengxin Wu , Ziye Chen , Guang Yang , Mingshu Zhao

For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…

Exactly Solvable and Integrable Systems · Physics 2026-03-03 Andrei D. Polyanin

The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\"odinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase is linear in the position, this latter…

Mathematical Physics · Physics 2016-08-16 M. Hassaïne P. A. Horváthy , J. -C. Yéra

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

We study well-posedness, local and global, existence of solutions for a general class of physically meaningful nonlinear Schr\"odinger systems with magnetic field involving local and nonlocal nonlinearities.

Functional Analysis · Mathematics 2010-04-27 Hichem Hajaiej

We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…

Mathematical Physics · Physics 2017-05-30 Qutaibeh D. Katatbeh , Dimitris M. Christodoulou

The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is an integrable extension of the standard NLS equation. Its…

Exactly Solvable and Integrable Systems · Physics 2017-04-19 Xiao-Yong Wen , Zhenya Yan , Yunqing Yang

The focusing nonlinear Schrodinger equation possesses special non-dispersive solitary type solutions, solitons. Under certain spectral assumptions we show existence and asymptotic stability of solutions with the asymptoic profile (as time…

Analysis of PDEs · Mathematics 2007-05-23 I. Rodnianski , W. Schlag , A. Soffer