NUMERICAL SIMULATIONS OF THE ENERGY-SUPERCRITICAL NONLINEAR SCHRÖDINGER EQUATION

DOI10.1142/S0219891610002104zbMath1403.37082arXiv0907.3130OpenAlexW2963368087WikidataQ115245252 ScholiaQ115245252MaRDI QIDQ3585518

Gideon Simpson, James E. Colliander, Catherine Sulem

Publication date: 20 August 2010

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.3130

zbMATH Keywords

global well-posednessnumerical simulationsnonlinear Schrödingerenergy supercritical

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)

Related Items

Large deviations principle for the cubic NLS equation ⋮ Numerical simulations for the energy-supercritical nonlinear wave equation ⋮ Going beyond the threshold: scattering and blow-up in the focusing NLS equation ⋮ On blow up for the energy super critical defocusing nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Dispersive estimates and the 2D cubic NLS equation.
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Nonlinear scattering theory at low energy
• Numerical solution of a nonlinear Klein-Gordon equation
• Decay and scattering of solutions of a nonlinear Schrödinger equation
• On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
• Scattering in the energy space and below for 3D NLS
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Algorithms to numerically evaluate the Hankel transform
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• On nonlinear schrödinger equations
• Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ³