Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System

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 ton-soliton solutions. Whenn=1andn=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.