Local and Nonlocal Reductions of Two Nonisospectral Ablowitz-Kaup-Newell-Segur Equations and Solutions

In this paper, local and nonlocal reductions of two nonisospectral Ablowitz-Kaup-Newell-Segur equations, the third order nonisospectral AKNS equation and the negative order nonisospectral AKNS equation, are studied. By imposing constraint conditions on the double Wronskian solutions of the aforesaid nonisospectral AKNS equations, various solutions for the local and nonlocal nonisospectral modified Korteweg-de Vries equation and local and nonlocal nonisospectral sine-Gordon equation are derived, including soliton solutions and Jordan block solutions. Dynamics of some obtained solutions are analyzed and illustrated by asymptotic analysis.

Automated summary

This paper examines local and nonlocal reductions of two nonisospectral Ablowitz-Kaup-Newell-Segur equations, resulting in various solutions for the modified Korteweg-de Vries equation and sine-Gordon equation, including solitons and Jordan block solutions. The dynamics of these solutions are analyzed and illustrated through asymptotic analysis.