Solutions and continuum limits to nonlocal discrete modified Korteweg de-Vries equations

2023/02/12 by Zhao, Song-lin, Xiang, Xiao-bo, Shen, Shou-feng
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2302.05843

Abstract

In this paper, we take advantage of the bilinearization reduction method to consider the local and nonlocal reduction of a discrete Ablowitz-Kaup-Newell-Segur equation. Exact solutions in double Casoratian form to the reduced nonlocal discrete modified Korteweg de-Vries equations are constructed. The dynamics of soliton solutions are analyzed and illustrated by asymptotic analysis. Moreover, both semi-continuous limit and full continuous limit, are applied to obtain the local and nonlocal semi-discrete modified Korteweg de-Vries equations, as well as the local and nonlocal continuous modified Korteweg de-Vries equations.

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