Discrete rogue waves and blow-up from solitons of a nonisospectral semi-discrete nonlinear Schrödinger equation

Abstract

We investigate the nonisospectral effects of a semi-discrete nonlinear Schrödinger 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 $t$.

10 pages, 9 figures

References in corpus (1)

• The role of multiple soliton and breather interactions in generation of rogue waves: the mKdV framework