Interaction with an obstacle in the 2D focusing nonlinear Schrödinger equation
DOI10.1007/s10444-023-10055-xzbMath1527.35383arXiv2102.02170OpenAlexW3127222049MaRDI QIDQ6083217
Oussama Landoulsi, Svetlana Roudenko, Kai Yang
Publication date: 31 October 2023
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.02170
Asymptotic behavior of solutions to PDEs (35B40) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Finite difference methods for boundary value problems involving PDEs (65N06) Boundary value problems on manifolds (58J32) Perturbations of PDEs on manifolds; asymptotics (58J37) Blow-up in context of PDEs (35B44) Traveling wave solutions (35C07) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Integro-partial differential equations (35R09)
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Cites Work
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- Petviashvilli's method for the Dirichlet problem
- On the Schrödinger equation outside strictly convex obstacles
- Scattering for the focusing energy-subcritical nonlinear Schrödinger equation
- Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary
- On the energy critical Schrödinger equation in 3D non-trapping domains
- Spherical means and radiation conditions
- Nonlinear Schrödinger equations and sharp interpolation estimates
- Nonlinear scalar field equations. I: Existence of a ground state
- Global well-posedness and scattering for the mass critical nonlinear Schrödinger equation with mass below the mass of the ground state
- Threshold solutions for the focusing 3D cubic Schrödinger equation
- Scattering for the nonradial 3D cubic nonlinear Schrödinger equation
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Finite-difference solutions of a non-linear Schrödinger equation
- On nonlinear Schrödinger equations in exterior domains
- Numerical study of Zakharov-Kuznetsov equations in two dimensions
- On blow-up solutions to the nonlinear Schrödinger equation in the exterior of a convex obstacle
- Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle
- Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study
- Blow-up dynamics in the mass super-critical NLS equations
- Construction of a solitary wave solution of the nonlinear focusing Schrödinger equation outside a strictly convex obstacle in the \(L^2\)-supercritical case
- Global existence for defocusing cubic NLS and Gross-Pitaevskii equations in three dimensional exterior domains
- A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
- Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
- The Focusing Cubic NLS on Exterior Domains in Three Dimensions
- Global Behavior of Finite Energy Solutions to the d-Dimensional Focusing Nonlinear Schrodinger Equation
- Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods
- The decay of solutions of the exterior initial-boundary value problem for the wave equation
- Precise smoothing effect in the exterior of balls
- Bilinear virial identities and applications
- Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- The exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle
- Finite difference discretization of the cubic Schrödinger equation
- Decay of solutions of the wave equation outside nontrapping obstacles
- Schéma de relaxation pour l'équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson
- Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
- Riesz Transforms Outside a Convex Obstacle
- Blow-up dynamics and spectral property in the L 2-critical nonlinear Schrödinger equation in high dimensions
- A Relaxation Scheme for the Nonlinear Schrödinger Equation
- Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations
- On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation
- Exponential decay of solutions of the wave equation in the exterior of a star‐shaped obstacle
- The limiting amplitude principle
