Smooth multisoliton solutions of the Geng-Xue equation
Nianhua Li, Q.P. Liu
TL;DR
This paper introduces a reciprocal transformation approach to derive smooth multisoliton solutions for the Geng-Xue equation, linking it to the Boussinesq hierarchy and providing explicit parametric representations.
Contribution
It develops a novel reciprocal transformation method to obtain explicit multisoliton solutions for the Geng-Xue equation, expanding solution techniques for integrable systems.
Findings
Derived a reciprocal transformation linking Geng-Xue to Boussinesq hierarchy.
Obtained explicit parametric forms for multisoliton solutions.
Extended the method to related equations like Degasperis-Procesi and Novikov.
Abstract
We present a reciprocal transformation which links the Geng-Xue equation to a particular reduction of the first negative flow of the Boussinesq hierarchy. We discuss two reductions of the reciprocal transformation for the Degasperis-Procesi and Novikov equations, respectively. With the aid of the Darboux transformation and the reciprocal transformation, we obtain a compact parametric representation for the smooth soliton solutions such as multi-kink solutions of the Geng-Xue equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Nonlinear Photonic Systems