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

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.