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Related papers: Vector NLS solitons interacting with a boundary

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I analyze the one-dimensional, cubic Schr\"odinger equation, with nonlinearity constructed from the current density, rather than, as is usual, from the charge density. A soliton solution is found, where the soliton moves only in one…

High Energy Physics - Theory · Physics 2015-06-26 R. Jackiw

We derive generalized nonlinear wave solution formula for mixed coupled nonlinear Sch\"odinger equations (mCNLSE) by performing the unified Darboux transformation. We give the classification of the general soliton formula on the nonzero…

Exactly Solvable and Integrable Systems · Physics 2015-11-06 Liming Ling , Li-Chen Zhao , Boling Guo

Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of…

The unified transform method is used to analyze the initial-boundary value problem for the coupled derivative nonlinear Schr\"odinger(CDNLS) equations on the half-line. In this paper, we assume that the solution $u(x,t)$ and $v(x,t)$ of…

Exactly Solvable and Integrable Systems · Physics 2018-12-19 Beibei Hu , Tiecheng Xia , Ning Zhang

In this article we apply quaternionic linear algebra and quaternionic linear system theory to develop the inverse scattering transform theory for the nonlinear Schr\"odinger equation with nonvanishing boundary conditions. We also determine…

Mathematical Physics · Physics 2023-03-17 Francesco Demontis , Cornelis van der Mee

We show the complete integrability and the existence of optical solitons of higher order nonlinear Schrodinger equation by inverse scattering method for a wide range of values of coefficients. This is achieved first by invoking a novel…

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

We consider the nonlinear Schr\"{o}dinger (NLS) equation on the half-line subjecting to a class of boundary conditions preserve the integrability of the model. For such a half-line problem, the Poisson brackets of the corresponding…

Exactly Solvable and Integrable Systems · Physics 2024-07-10 Baoqiang Xia

We consider the nonlinear Schr\"odinger equation on a unit ball in one and two dimensions with Dirichlet boundary conditions, which have stabilizing effect on solutions behavior. In particular, we confirm that the ground state solutions are…

Analysis of PDEs · Mathematics 2025-10-29 Christian Klein , Svetlana Roudenko , Nikola Stoilov

We investigate the spectral stability of non-degenerate vector soliton solutions and the nonlinear stability of breather solutions for the coupled nonlinear Schrodinger (CNLS) equations. The non-degenerate vector solitons are spectrally…

Exactly Solvable and Integrable Systems · Physics 2024-11-14 Liming Ling , Dmitry E. Pelinovsky , Huajie Su

The Boltzmann type kinetic equation for solitons in Nonlinear Schr\"{o}dinger equation has been constructed on the base of analysis of two soliton collision. Possible applications for Langmuir solitons in plasma and solitons in optic fiber…

Statistical Mechanics · Physics 2008-02-03 I. V. Baryakhtar

Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and photorefractive materials, the vector solitons…

Pattern Formation and Solitons · Physics 2021-06-29 S. Stalin , R. Ramakrishnan , M. Lakshmanan

Binary Bargmann symmetry constraints are applied to decompose soliton equations into finite-dimensional Liouville integrable Hamiltonian systems, generated from so-called constrained flows. The resulting constraints on the potentials of…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Wen-Xiu Ma

Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be…

Computational Engineering, Finance, and Science · Computer Science 2024-08-20 Erik Faust , Alexander Schlüter , Henning Müller , Ralf Müller

We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundary of which is delineated both by ground state solitons and…

Analysis of PDEs · Mathematics 2025-09-19 Alex H. Ardila , Jason Murphy

We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We…

Analysis of PDEs · Mathematics 2009-10-12 Claudio Bonanno

We consider the discrete and continuous vector non-linear Schrodinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in…

Mathematical Physics · Physics 2017-03-14 Panagiota Adamopoulou , Anastasia Doikou , Georgios Papamikos

In the first part of this article we deal with the existence of at least three non-trivial weak solutions of a nonlocal problem with nonstandard growth involving a nonlocal Robin type boundary condition. The second part of the article is…

Analysis of PDEs · Mathematics 2020-03-31 Sabri Bahrouni , Ariel Salort

Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully…

Soft Condensed Matter · Physics 2015-05-27 J. P. Bardhan , D. A. Tejani , N. S. Wieckowski , A. Ramaswamy , M. G. Knepley

In this work, we consider an integrable three-component coupled Hirota (tcCH) equations in detail via the Riemann-Hilbert (RH) approach. We present some properties of the spectral problems of the tcCH equations with $4\times4$ the Lax pair.…

Exactly Solvable and Integrable Systems · Physics 2019-11-11 Xin Wu , Shou-Fu Tian , Jin-Jie Yang

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