Discrete rogue waves and blow-up from solitons of a nonisospectral semi-discrete nonlinear Schr\"{o}dinger equation

TL;DR

This paper studies a semi-discrete nonlinear Schrödinger equation, revealing how nonisospectral effects lead to rogue waves and finite-time blow-up phenomena, with solutions analyzed through bilinear forms and Casoratian techniques.

Contribution

It introduces a new integrable semi-discrete model and analyzes its solutions, showing rogue wave formation and blow-up behavior due to nonisospectral effects.

Findings

Solutions exhibit rogue wave behavior and blow-up at finite times.

The bilinear form and Casoratian solutions facilitate analysis of dynamics.

Nonisospectral effects significantly influence solution behavior.

Abstract

We investigate the nonisospectral effects of a semi-discrete nonlinear Schr\"{o}dinger equation, which is a direct integrable discretisation of its continuous counterpart. Bilinear form and double casoratian solution of the equation are presented. Dynamics of solutions are analyzed. Both solitons and multiple pole solutions admit space-time localized rogue wave behavior. And more interestingly, the solutions allow blow-up at finite time $t$.