# Rational solutions for three semi-discrete modified Korteweg-de Vries type equations

## TL;DR

This paper derives rational solutions for three semi-discrete modified Korteweg-de Vries type equations using Casorati determinants and analyzes their asymptotic behavior to understand their dynamics.

## Contribution

It introduces explicit rational solutions for three semi-discrete mKdV equations using Casorati determinants, advancing the understanding of their solution structures.

## Key findings

- Explicit rational solutions derived for three semi-discrete mKdV equations.
- Asymptotic analysis reveals the dynamics of some rational solutions.
- Provides a systematic approach to solutions using Casorati determinants.

## Abstract

In this paper, we consider three semi-discrete modified Korteweg-de Vries type equations which are the nonlinear lumped self-dual network equation,the semi-discrete lattice potential modified Korteweg-de Vries equation and a semi-discrete modified Korteweg-de Vries equation. We derive several kinds of exact solutions, in particular rational solutions, in terms of the Casorati determinant for these three equations respectively. For some rational solutions, we present the related asymptotic analysis to understand their dynamics better.