Mixed spectral AKNS hierarchy from linear isospectral problemand its exact solutions

Open Physics

卷:13

Zhang Sheng¹  Gao Xu-Dong² 

[1] School of Mathematicsand Physics, Bohai University, Jinzhou 121013, PR China;

[2] School of Mathematics and Statistics, Kashgar University,Kashgar 844066, Peoples’s Republic of China;

关键词: mixed spectral AKNS hierarchy;    spectral problem;    exact solution;    soliton solution;    inverse scatteringtransformation;   

DOI  :  10.1515/phys-2015-0040

来源: DOAJ

【 摘 要 】

In this paper, the AKNS isospectral problem andits corresponding time evolution are generalized by embeddingthree coefficient functions. Starting from the generalizedAKNSisospectral problem, a mixed spectralAKNShierarchy with variable coefficients is derived. Thanks tothe selectivity of these coefficient functions, the mixedspectral AKNS hierarchy contains not only isospectralequations but also nonisospectral equations. Based on asystematic analysis of the related direct and inverse scatteringproblems, exact solutions of the mixed spectralAKNS hierarchy are obtained through the inverse scatteringtransformation. In the case of reflectionless potentials,the obtained exact solutions are reduced to n-soliton solutions.This paper shows that the AKNS spectral problembeing nonisospectral is not a necessary condition toconstruct a nonisospectral AKNS hierarchy and that theinverse scattering transformation can be used for solvingsome other variable-coefficient mixed hierarchies ofisospectral equations and nonisospectral equations.

【 授权许可】

Unknown