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Complexity
Volume 2017, Article ID 9457078, 10 pages
https://doi.org/10.1155/2017/9457078
Research Article

Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System

School of Mathematics and Physics, Bohai University, Jinzhou 121013, China

Correspondence should be addressed to Sheng Zhang; moc.621@anihcgnahzs

Received 29 April 2017; Accepted 9 October 2017; Published 6 November 2017

Academic Editor: Pietro De Lellis

Copyright © 2017 Sheng Zhang and Siyu Hong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform (IST) method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced to -soliton solutions. When and , the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.