Prolongation Approach to B\"{a}cklund Transformation of Zhiber-Mikhailov-Shabat Equation
Huan-xiong Yang, You-Quan Li
TL;DR
This paper develops a prolongation approach to derive a Bäcklund transformation for the Zhiber-Mikhailov-Shabat equation, enhancing understanding of its integrable structure through Wahlquist-Estabrook's method.
Contribution
It introduces a prolongation-based method to obtain an auto-Bäcklund transformation for the ZMS equation, linking prolongation structures with Lax pairs and Riccati equations.
Findings
Derived Lax pair for ZMS equation
Formulated Riccati equations for pseudopotentials
Obtained an auto-Bäcklund transformation
Abstract
The prolongation structure of Zhiber-Mikhailov-Shabat (ZMS) equation is studied by using Wahlquist-Estabrook's method. The Lax-pair for ZMS equation and Riccati equations for pseudopotentials are formulated respectively from linear and nonlinear realizations of the prolongation structure. Based on nonlinear realization of the prolongation structure, an auto-Bcklund transformation of ZMS equation is obtained.
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