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arXiv · 2302.05843

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

Song-lin Zhao·Xiao-bo Xiang·Shou-feng Shen
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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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Song-lin Zhao, Xiao-bo Xiang, Shou-feng Shen. 2023-02-12. Solutions and continuum limits to nonlocal discrete modified Korteweg de-Vries equations. https://arxiv.org/abs/2302.05843

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