Abstract
We investigate the nonisospectral effects of a semi-discrete nonlinear Schrödinger equation, which is a direct integrable discretization 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.
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