The discrete complex Ginzburg–Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of survival/destruction of localised structures in many physical situations. In this work, we prove that in the...
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May 4, 2023 (v1)PublicationUploaded on: May 5, 2023
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January 16, 2023 (v1)Publication
The Ablowitz–Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localized solitons to rational solutions in the form of the spatiotemporally localized discrete Peregrine soliton. Proving a closeness result between the solutions of the Ablowitz–Ladik system...
Uploaded on: March 3, 2023 -
March 22, 2022 (v1)Publication
While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger equation, which is more significant for physical applications, is not. We prove closeness of the solutions of both systems in the sense of a "continuous dependence" on their initial data in the and metrics. The most striking relevance of the analytical results...
Uploaded on: December 4, 2022