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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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2191-0294
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Volume 19, Issue 3-4

Issues

Lax Integrability and Exact Solutions of a Variable-Coefficient and Nonisospectral AKNS Hierarchy

Sheng Zhang / Siyu Hong
Published Online: 2018-04-19 | DOI: https://doi.org/10.1515/ijnsns-2016-0191

Abstract

In this paper, a variable-coefficient and nonisospectral Ablowitz–Kaup–Newell–Segur (vcniAKNS) hierarchy with Lax integrability is constructed by embedding a finite number of differentiable and time-dependent functions into the well-known AKNS spectral problem and its time evolution equation. In the framework of inverse scattering transform method with time-varying spectral parameter, the constructed vcniAKNS hierarchy is solved exactly. As a result, exact solutions and their reduced n-soliton solutions of the vcniAKNS hierarchy are obtained. It is graphically shown that the parity of an embedded time-dependent function has connection with the symmetrical characteristics of the spatial structures and singular points of the obtained one-soliton solutions.

Keywords: lax integrability; exact solution; soliton solution; vcniAKNS hierarchy; inverse scattering transform

PACS: 05.45.Yv; 04.20.Jb; 02.30.Jr

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About the article

Received: 2016-12-26

Accepted: 2017-11-20

Published Online: 2018-04-19

Published in Print: 2018-06-26


This work was supported by the Natural Science Foundation of China (11547005), the Natural Science Foundation of Liaoning Province of China (20170540007), the Natural Science Foundation of Education Department of Liaoning Province of China (LZ2017002) and Innovative Talents Support Program in Colleges and Universities of Liaoning Province (LR2016021).


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 3-4, Pages 1–12, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0191.

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