Accurate and efficient numerical methods for the nonlinear Schrödinger equation with Dirac delta potential

DOI10.1007/s10092-023-00551-3zbMath1529.35485OpenAlexW4388825972MaRDI QIDQ6142563

Xing Dong Tang, Yong-Yong Cai, Gui Xiang Xu, Xuanxuan Zhou

Publication date: 4 January 2024

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-023-00551-3

zbMATH Keywords

convergence analysisfinite difference methodnonlinear Schrödinger equationorbital stabilityChebyshev collocation methodDirac delta potentialconservative propertiesinner boundary conditions

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Blow-up in context of PDEs (35B44) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• Global dynamics below the standing waves for the focusing semilinear Schrödinger equation with a repulsive Dirac delta potential
• Instability of bound states for abstract nonlinear Schrödinger equations
• Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential
• Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials
• Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential
• An accurate conservative level set/ghost fluid method for simulating turbulent atomization
• Nonlinear Schrödinger equation with a point defect
• An explicit jump immersed interface method for two-phase Navier-Stokes equations with interfaces
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• Numerical analysis of blood flow in the heart
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Regularization techniques for numerical approximation of PDEs with singularities
• EJIIM for the stationary Schrödinger equations with delta potential wells
• Conservative modified Crank-Nicolson and time-splitting wavelet methods for modeling Bose-Einstein condensates in delta potentials
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Strong NLS soliton-defect interactions
• Mathematical theory and numerical methods for Bose-Einstein condensation
• A high order compact FD framework for elliptic BVPs involving singular sources, interfaces, and irregular domains
• Instability of the solitary waves for the 1d NLS with an attractive delta potential in the degenerate case
• Nonoverlapping localized exponential time differencing methods for diffusion problems
• A ghost fluid/level set method for boiling flows and liquid evaporation: application to the leidenfrost effect
• Scattering for NLS with a delta potential
• Soliton splitting by external delta potentials
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data
• The immersed boundary method
• Some Nonoverlapping Domain Decomposition Methods
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Weak multi-symplectic reformulation and geometric numerical integration for the nonlinear Schrödinger equations with delta potentials
• Bound and resonance states of the nonlinear Schrödinger equation in simple model systems
• Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method
• The transition from diffusion to blow-up for a nonlinear Schrödinger equation in dimension 1

This page was built for publication: Accurate and efficient numerical methods for the nonlinear Schrödinger equation with Dirac delta potential