Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line

DOI10.3934/dcdss.2021030zbMath1487.35349OpenAlexW3151706366MaRDI QIDQ2673647

Mostafa Abounouh, Abderrazak Chrifi, Hassan Al Moatassime

Publication date: 10 June 2022

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2021030

zbMATH Keywords

Galerkin methodnonlinear Schrödinger equationfractional derivativeartificial boundary condition

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Cites Work

• Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential
• Finite dimensional behavior for weakly damped driven Schrödinger equations
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Artificial boundary condition for one-dimensional nonlinear Schrödinger problem with Dirac interaction: existence and uniqueness results
• Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line
• Discrete transparent boundary conditions for the numerical solution of Fresnel's equation
• Strong NLS soliton-defect interactions
• Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations
• Structure of a quantized vortex in boson systems
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
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