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

2025/08/29 by Mengli Tian, Tian, Mengli, Chunxia Li +7
Mathematics · Physics and Astronomy · #35A25 #37K10 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2508.21434

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• From the self-dual Yang-Mills equation to the Fokas-Lenells equation
• Inverse scattering transform for integrable nonisospectral hierarchy associate with Camassa-Holm equation
• Cauchy matrix approach to the SU(2) self-dual Yang--Mills equation

Related

• Darboux Transformation for the Nonisospectral and Variable-coefficient KdV Equation
• Solitons and breathers for nonisospectral mKdV equation with Darboux transformation
• Nonlocal Modified KdV Equations and Their Soliton Solutions
• Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence
• Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform