Integrable mKdV Models as Reductions of AKNS Integrable Systems via Dual Similarity Transformations

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Abstract

This paper explores integrable modified Korteweg-de Vries (mKdV) models using dual similarity transformations. Two representative examples involving distinct similarity transformations are presented, along with their corresponding reduced Ablowitz-Kaup-Newell–Segur matrix spectral problems. These examples illustrate how reduced matrix mKdV integrable models can be systematically generated through such transformations.

Keywords:

Lax pair AKNS matrix spectral problem zero-curvature equation integrable hierarchy similarity transformation

Author Biography

  • Wen-Xiu Ma

    Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

    Research Center of Astrophysics and Cosmology, Khazar University, Baku 1096, Azerbaijan

    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

    Material Science Innovation and Modelling, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

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DOI

10.4208/eajam.2025-103.181125