Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations

Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations Nonlinear Dyn https://doi.org/10.1007/s11071-018-4373-0 ORIGINAL PAPER Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations Bo Yang · Yong Chen Received: 15 February 2018 / Accepted: 14 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract A study of high-order solitons in three non- Keywords Nonlocal nonlinear Schrödinger equa- local nonlinear Schrödinger equations is presented. tions · High-order soliton · Riemann–Hilbert method These include the PT -symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schrödinger equations. General high-order solitons in three different 1 Introduction equations are derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except for the differ- The integrable nonlinear wave equations and soliton ence in the corresponding symmetry relations on the theory have been studied for many years [1–5]. They “perturbed” scattering data. Dynamics of general high- are significant subjects in many branches of nonlin- order solitons in these equations is further analyzed. ear science. For the integrable nonlinear models, most It is shown that the high-order fundamental-soliton is of them are local equations, i.e., the solutions evolu- moving on several different trajectories in nearly equal tion depends only on the local solution value with its local space and time derivatives. Recently, a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations

Yang, Bo; Chen, Yong
Nonlinear Dynamics , Volume OnlineFirst – May 29, 2018
14 pages
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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-018-4373-0
Publisher site
See Article on Publisher Site

Abstract

Nonlinear Dyn https://doi.org/10.1007/s11071-018-4373-0 ORIGINAL PAPER Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations Bo Yang · Yong Chen Received: 15 February 2018 / Accepted: 14 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract A study of high-order solitons in three non- Keywords Nonlocal nonlinear Schrödinger equa- local nonlinear Schrödinger equations is presented. tions · High-order soliton · Riemann–Hilbert method These include the PT -symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schrödinger equations. General high-order solitons in three different 1 Introduction equations are derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except for the differ- The integrable nonlinear wave equations and soliton ence in the corresponding symmetry relations on the theory have been studied for many years [1–5]. They “perturbed” scattering data. Dynamics of general high- are significant subjects in many branches of nonlin- order solitons in these equations is further analyzed. ear science. For the integrable nonlinear models, most It is shown that the high-order fundamental-soliton is of them are local equations, i.e., the solutions evolu- moving on several different trajectories in nearly equal tion depends only on the local solution value with its local space and time derivatives. Recently, a

Journal

Nonlinear Dynamics – Springer Journals

Published: May 29, 2018

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