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

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.

arXiv comment16 pages, 16 figures

References in corpus (7)

• Complexiton Solutions of the Toda Lattice Equation
• Wronskians, Generalized Wronskians and Solutions to the Korteweg-de Vries Equation
• The role of multiple soliton and breather interactions in generation of rogue waves: the mKdV framework
• Notes on solutions in Wronskian form to soliton equations: KdV-type
• On the dynamics of rational solutions for 1-D generalized Volterra system
• On a class of rational and mixed soliton-rational solutions of Toda lattice
• The discrete mKdV equation revisited: a Riemann-Hilbert approach