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

TL;DR

This paper develops exact solutions for nonlocal discrete modified Korteweg de-Vries equations using bilinearization, and explores their continuum limits to connect discrete and continuous models.

Contribution

It introduces a bilinearization reduction method to derive exact solutions for nonlocal discrete MKdV equations and analyzes their continuum limits.

Findings

Exact double Casoratian solutions for nonlocal discrete MKdV equations

Analysis of soliton dynamics via asymptotic methods

Derivation of semi-discrete and continuous limits for local and nonlocal cases

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.