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

2023/06/08 by Ke Yan, Yingying Sun, Yan, Ke +3
Mathematics · Physics and Astronomy · #39A14 #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2306.04867

openalex publication_date 2023/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Z², which demonstrate periodic structure.

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