Backlund transformation of the Geng-Xue system
Lihua Wu, Nianhua Li
TL;DR
This paper develops a Backlund transformation for the Geng-Xue system using reciprocal and gauge transformations, derives N-Backlund transformations, and finds exact solutions including multi-kink and solitons, also discussing related equations.
Contribution
It introduces a novel Backlund transformation for the Geng-Xue system and extends it to N-Backlund transformations, providing new exact solutions and insights into related equations.
Findings
Constructed Backlund transformation for Geng-Xue system
Derived N-Backlund transformation via Bianchi's permutability
Obtained multi-kink and soliton solutions
Abstract
We construct a Backlund transformation for the Geng-Xue system with the help of reciprocal and gauge transformations. Furthermore, we derive N-Backlund transformation for the Geng-Xue system resorting to Bianchi's permutability. As an application, we obtain some exact solutions of the Geng-Xue system including multi-kink, bell-shaped soliton. Finally, we discuss Backlund transformations for the Degasperis-Procesi and the Novikov equations, which are two reductions of the Geng-Xue system.
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Taxonomy
TopicsNonlinear Waves and Solitons · Fractional Differential Equations Solutions · Algebraic structures and combinatorial models