Two integrable differential-difference equations derived from NLS-type equation

TL;DR

This paper derives two new integrable differential-difference equations from known (2+1)-dimensional equations, constructs multi-soliton solutions, and analyzes their interaction behaviors through asymptotic analysis and graphical demonstrations.

Contribution

It introduces two novel integrable differential-difference equations derived from established (2+1)D equations and provides explicit multi-soliton solutions with interaction analysis.

Findings

Multi-soliton solutions are explicitly constructed.

Elastic and inelastic soliton interactions are characterized.

Graphical dynamics of two-soliton solutions are presented.

Abstract

Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted semi-discrete systems are given through Hirota's bilinear method. Elastic and inelastic interaction behavior between two solitons are studied through the asymptotic analysis. Dynamics of two-soliton solutions are shown with graphs.