Cauchy matrix structures and solutions to the nonisospectral three-component mKdV equations

Abstract

Nonisospectral integrable systems can describe solitary waves in nonuniform media. In this paper, we apply the Cauchy matrix approach to construct three types of nonisospectral matrix modified Korteweg-de Vries (mKdV) eqautions and present their Cauchy matrix structures and solutions. Further, through complex reduction, we further obtain three nonisospectral three-component mKdV (NTCmKdV) equations, which can be regarded as novel members of the nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. In particular, the explicit solutions are given for the soliton solutions, and the double-pole solutions, respectively. The dynamical behaviors of these solutions are analyzed to reveal the influence of nonisospectral terms on the solution structure.