Integrable discretization of nonlinear Schrödinger equation and its application with Fourier pseudo-spectral method
DOI10.1007/s11075-014-9928-7zbMath1322.65097OpenAlexW2127825545MaRDI QIDQ494675
Ying-Nan Zhang, Hon-Wah Tam, Xing-Biao Hu
Publication date: 1 September 2015
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-014-9928-7
nonlinear Schrödinger equationintegrable discretizationnumerical resultFourier pseudo-spectral methodinfinite conservation quantities
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Integrable nonlinear Schrödinger systems and their soliton dynamics
- On the preservation of phase space structure under multisymplectic discretization
- Analytical and numerical aspects of certain nonlinear evolution equations. I. Analytical
- Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
- Numerical methods for the nonlinear Schrödinger equation with nonzero far-field conditions
- Linear integral equations and nonlinear difference-difference equations
- Finite-difference solutions of a non-linear Schrödinger equation
- Bäcklund transformations and their applications
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- Hirota equation as an example of an integrable symplectic map
- The problem of integrable discretization: Hamiltonian approach
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation
- On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
- Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
- Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
- Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation
- Nonlinear Waves in Integrable and Nonintegrable Systems
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
- On Homoclinic Structure and Numerically Induced Chaos for the Nonlinear Schrödinger Equation
- Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
- Dark solitons in atomic Bose–Einstein condensates: from theory to experiments
- Method for Generating Discrete Soliton Equation. III
- Method for Generating Discrete Soliton Equations. IV
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- Bäcklund transformations and nonlinear differential difference equations
- Nonlinear differential difference equations as Backlund transformations
- An Envelope Soliton Problem
- Integrable three-dimensional lattices
- Finite difference discretization of the cubic Schrödinger equation
- Nonlinear differential−difference equations
- Generating exactly soluble nonlinear discrete evolution equations by a generalized Wronskian technique
- Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
- On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation
- Loop groups and discrete KdV equations
- Integrable discretization of ‘time’ and its application on the Fourier pseudospectral method to the Korteweg–de Vries equation
- Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
- Geometric integrators for the nonlinear Schrödinger equation
This page was built for publication: Integrable discretization of nonlinear Schrödinger equation and its application with Fourier pseudo-spectral method
