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N-Soliton Solutions for the NLS-Like Equation and Perturbation Theory Based on the Riemann–Hilbert Problem

Symmetry, 2019
In this paper, a kind of nonlinear Schrödinger (NLS) equation, called an NLS-like equation, is Riemann–Hilbert investigated. We construct a 2 × 2 Lax pair associated with the NLS equation and combine the spectral analysis to ...
Yong Fang, Yuxin Lin, Huanhe Dong
exaly   +2 more sources

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Validity of Whitham’s Equations for the Modulation of Periodic Traveling Waves in the NLS Equation

Journal of Nonlinear Science, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wolf-Patrick Düll, Guido Schneider
openaire   +3 more sources

Whiskered Tori for NLS Equations

1993
Spectral theory is used to display instabilities and hyperbolic structure for certain periodic soliton equations, as well as to generate representations of whiskered tori for these equations. The NLS equation is discussed as a primary model, with references to other equations which possess a similar hyperbolic structure.
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The Nonlinear Schrödinger (NLS) Equation

Abstract The nonlinear Schrödinger (NLS) equation is a universal, lowest order (normal form) model for the evolution of modulated envelope waves in nonlinear media. As such, it is a fundamental model appearing at the heart of an extremely wide variety of physical contexts.
R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis   +2 more
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Dispersive estimates and the 2D cubic NLS equation

Journal d'Analyse Mathématique, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multicomponent NLS Type Equations and BECs

2019
To investigate the dynamical behaviors of multi-species Bose–Einstein condensates in an optical lattice, we consider, in this chapter, the multicomponent nonlinear Schrodinger type equations. We successively study the phase diagram for superfluid and insulator phases of two-species BECs in a one-dimensional optical lattice, the vector solitons and ...
Wu-Ming Liu, Emmanuel Kengne
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‘‘Polynomial constants’’ for the quantized NLS equation

Journal of Mathematical Physics, 1984
The classical nonlinear Schrödinger equation (NLS) is known to have an infinite number of polynomial constants. While recursion relations to compute these are available, no general expressions in terms of the fields have been found. However, general expressions have been obtained in terms of the reflection coefficients. When we turn to the quantum case
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Special Solutions of some Generalized NLS Equations

2009
Using a Madelung fluid description a discussion is given for some generalized NLS equations. Solitary wave and periodic solutions are obtained for constant and stationary profile current velocity.
Visinescu A, Grecu D, Fedele R, De Nicola S   +3 more
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Dbar‐approach to coupled nonlocal NLS equation and general nonlocal reduction

Studies in Applied Mathematics, 2022
Junyi Zhu
exaly  

Darboux transformation and soliton solutions for nonlocal Kundu-NLS equation

Nonlinear Dynamics, 2022
Ruiqi Wang
exaly