Error propagation in the numerical integration of solitary waves. The regularized long wave equation
From MaRDI portal
Publication:5928461
DOI10.1016/S0168-9274(99)00148-8zbMath0972.65062MaRDI QIDQ5928461
Publication date: 11 November 2001
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
relative equilibriasolitary wavesconservative methodserror propagationHamiltonian structureregularized long wave equationsymmetry groups
PDEs in connection with fluid mechanics (35Q35) Solitary waves for incompressible inviscid fluids (76B25) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)
Related Items
Numerical simulation and convergence analysis of a high-order conservative difference scheme for SRLW equation ⋮ Explicit finite difference methods for the EW and RLW equations ⋮ Conservative schemes for the symmetric regularized long wave equations ⋮ Numerical detection and generation of solitary waves for a nonlinear wave equation ⋮ Resolving entropy growth from iterative methods ⋮ A modified equation approach to selecting a nonstandard finite difference scheme applied to the regularized long wave equation ⋮ A decoupled and conservative difference scheme with fourth-order accuracy for the symmetric regularized long wave equations ⋮ A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations ⋮ Solitary waves of the EW and RLW equations ⋮ On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations ⋮ A Conservative Fully Discrete Numerical Method for the Regularized Shallow Water Wave Equations ⋮ Numerical behaviour of stable and unstable solitary waves
Cites Work
- Pseudo-spectral solution of nonlinear Schrödinger equations
- Invariants and numerical methods for ODEs
- Fourier pseudospectral solution of the regularised long wave equation
- Scattering of regularized-long-wave solitary waves
- Hamiltonian-conserving discrete canonical equations based on variational difference quotients
- Solitary waves of the equal width wave equation
- Numerical study of the regularized long-wave equation. II: Interaction of solitary waves
- Numerical solution of a nonlinear Klein-Gordon equation
- Asymptotic stability of solitary waves
- On the stability of solitary-wave solutions of model equations for long waves
- Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation
- Hamiltonian long-wave approximations to the water-wave problem
- The rate of error growth in Hamiltonian-conserving integrators
- Variable steps for reversible integration methods
- Accurate long-term integration of dynamical systems
- Solitary waves of the regularised long-wave equation
- The Development of Variable-Step Symplectic Integrators, with Application to the Two-Body Problem
- Solving Ordinary Differential Equations I
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
- Euler operators and conservation laws of the BBM equation
- The numerical integration of relative equilibrium solutions. Geometric theory
- Error Growth in the Numerical Integration of Periodic Orbits, with Application to Hamiltonian and Reversible Systems
- Asymptotic stability of solitary waves for the regularized long-wave equation
- Model equations for long waves in nonlinear dispersive systems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
