Numerical Study of a Nonlocal Nonlinear Schrödinger Equation (MMT Model)
Esfahani A. Muslu G.M.
March 2026John Wiley and Sons Inc
Studies in Applied Mathematics
2026#156Issue 3
In this paper, we study a nonlocal nonlinear Schrödinger equation (MMT model). We investigate the effect of the nonlocal operator appearing in the nonlinearity on the long-term behavior of solutions, and we identify the conditions under which the solutions of the Cauchy problem associated with this equation are bounded globally in time in the energy space. We also explore the dynamical behavior of standing wave solutions. Therefore, we first numerically generate standing wave solutions of nonlocal nonlinear Schrödinger equation by using the Petviashvilis iteration method and their stability is investigated by the split-step Fourier method. This equation also has a two-parameter family of standing wave solutions. In a second step, we meticulously concern with the construction and stability of a two-parameter family of standing wave solutions numerically. Finally, we investigate the semiclassical limit of the nonlocal nonlinear Schrödinger equation in both focusing and defocusing cases.
blowup , boosted standing wave , nonlocal nonlinear Schrödinger equation , Petviashvili iteration method , semiclassical limit , split-step Fourier method , stability , standing wave
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Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
School of Mathematics and Computer Science, Damghan University, Damghan, Iran
Department of Mathematics, Istanbul Technical University, Istanbul, Maslak, Turkey
Department of Mathematics
School of Mathematics and Computer Science
Department of Mathematics
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026