Solitary wave solutions for nonlinear fractional Schrödinger equation in Gaussian nonlocal media. (English) Zbl 1410.35222

Summary: This article is devoted to the study of nonlinear fractional Schrödinger equation with a Gaussian nonlocal response. We firstly prove the existence of solitary wave solutions by using the variational method and Mountain Pass Theorem. Numerical simulations are presented to verify the findings of the existence theorem. And we also investigate the impacts of Gaussian nonlocal response and fractional-order derivatives on the solitary waves, which enable us to perform control experiments for the development of rogue waves in quantum mechanics and optics.


35Q55 NLS equations (nonlinear Schrödinger equations)
35R11 Fractional partial differential equations
35C08 Soliton solutions
35A15 Variational methods applied to PDEs
81V80 Quantum optics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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