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arXiv · 2306.04867

Revisit to solutions for Adler-Bobenko-Suris lattice equations and lattice Boussinesq-type equations

Ke Yan·Ying-ying Sun·Song-lin Zhao
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Abstract

Solutions for all Adler-Bobenko-Suris equations excluding Q4 and several lattice Boussinesq-type equations are reconsidered by employing the Cauchy matrix approach. Through introducing a ``fake'' nonautonomous plane wave factor, we derive soliton solutions, oscillatory solutions, and semi-oscillatory solutions, for the target lattice equations. Unlike the conventional soliton solutions, the oscillatory solutions take constant values on all elementary quadrilaterals on Z^2, which demonstrate periodic structure.

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Ke Yan, Ying-ying Sun, Song-lin Zhao. 2023-06-08. Revisit to solutions for Adler-Bobenko-Suris lattice equations and lattice Boussinesq-type equations. https://arxiv.org/abs/2306.04867

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