标题： 柯西矩阵结构和非同谱三组分mKdV方程的解 显示英文标题

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

摘要： 非等谱可积系统可以描述非均匀介质中的孤立波。 在本文中，我们将柯西矩阵方法应用于构建三种类型的非等谱矩阵修正Korteweg-de Vries（mKdV）方程，并给出它们的柯西矩阵结构和解。 此外，通过复数约化，我们进一步得到三种非等谱三组分mKdV（NTCmKdV）方程，这些方程可以看作是非等谱Ablowitz-Kaup-Newell-Segur（AKNS）层次的新成员。 特别是，分别给出了孤子解和双极点解的显式解。 分析了这些解的动力学行为，以揭示非等谱项对解结构的影响。 显示英文摘要

摘要： 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.