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

Author:

Ke Yan, Ying-ying Sun, Song-lin Zhao

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI)

journal:

date:

2023-06-07 16:00:00

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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