Nonautonomous mixed mKdV-sinh-Gordon hierarchy
J.F. Gomes, G. R. de Melo, L.H. Ymai, A.H. Zimerman
TL;DR
This paper develops a nonautonomous mixed mKdV-sine-Gordon integrable model using affine Lie algebra techniques, providing a systematic soliton solution construction that captures transitions between different soliton types.
Contribution
It introduces a novel nonautonomous mixed mKdV-sine-Gordon hierarchy and adapts the dressing method for arbitrary time-dependent functions.
Findings
Constructed a nonautonomous mixed mKdV/sine-Gordon model.
Developed a systematic soliton solution method.
Described soliton transitions between pure mKdV and sine-Gordon systems.
Abstract
The construction of a nonautonomous mixed mKdV/sine-Gordon model is proposed by employing an infinite dimensional affine Lie algebraic structure within the zero curvature representation. A systematic construction of soliton solutions is provided by an adaptation of the dressing method which takes into account arbitrary time dependent functions. A particular choice of those arbitrary functions provides an interesting solution describing the transition of a pure mKdV system into a pure sine-Gordon soliton.
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