Geometric finite difference schemes for the generalized hyperelastic-rod wave equation
From MaRDI portal
Publication:629430
DOI10.1016/j.cam.2010.09.015zbMath1350.74026OpenAlexW2088415943MaRDI QIDQ629430
Publication date: 9 March 2011
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2010.09.015
BBM equationCamassa-Holm equationconservative schemesdiscrete gradientsmulti-symplecticityhyperelastic-rod wave
KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in solid mechanics (74S20)
Related Items (10)
Energy-preserving \(H^1\)-Galerkin schemes for shallow water wave equations with peakon solutions ⋮ A linearly implicit structure-preserving scheme for the Camassa-Holm equation based on multiple scalar auxiliary variables approach ⋮ A numerical study of variational discretizations of the Camassa-Holm equation ⋮ Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach ⋮ A high-order linearly implicit energy-preserving Partitioned Runge-Kutta scheme for a class of nonlinear dispersive equations ⋮ Invariants-preserving integration of the modified Camassa-Holm equation ⋮ Convergent numerical schemes for the compressible hyperelastic rod wave equation ⋮ Global attractor for the generalized hyperelastic-rod equation ⋮ A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation ⋮ Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A finite difference solution of the regularized long-wave equation
- A convergent numerical scheme for the Camassa-Holm equation based on multipeakons
- Global conservative solutions of the generalized hyperelastic-rod wave equation
- Multi-symplectic integration of the Camassa-Holm equation
- Stability of a class of solitary waves in compressible elastic rods
- An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations
- Wave breaking for nonlinear nonlocal shallow water equations
- Multisymplectic geometry, variational integrators, and nonlinear PDEs
- The Hamiltonian structure of the Camassa-Holm equation
- Backward error analysis for multi-symplectic integration methods
- Geodesic flow on the diffeomorphism group of the circle
- Numerical study of traveling-wave solutions for the Camassa--Holm equation
- Traveling waves in compressible elastic rods
- Integral and integrable algorithms for a nonlinear shallow-water wave equation
- Time integration and discrete Hamiltonian systems
- On the scattering problem for the Camassa-Holm equation
- A Local Discontinuous Galerkin Method for the Camassa–Holm Equation
- High-order compact difference scheme for the regularized long wave equation
- Numerical Methods for Evolutionary Differential Equations
- Evolution of the Scattering Coefficients of the Camassa–Holm Equation, for General Initial Data
- A Convergent Finite Difference Scheme for the Camassa–Holm Equation with General $H^1$ Initial Data
- On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
- Geometric integration using discrete gradients
- Multi-symplectic structures and wave propagation
- On the Inverse Scattering Approach to the Camassa-Holm Equation
- An integrable shallow water equation with peaked solitons
- The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
- On the Cauchy Problem for a Nonlinearly Dispersive Wave Equation
- Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
- On a Completely Integrable Numerical Scheme for a Nonlinear Shallow-Water Wave Equation
- Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
- Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation
- Model equations for long waves in nonlinear dispersive systems
- Convergence of a Finite Difference Scheme for the Camassa–Holm Equation
- Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
- Finite-difference schemes for nonlinear wave equation that inherit energy conservation property
- Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
- Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods.
This page was built for publication: Geometric finite difference schemes for the generalized hyperelastic-rod wave equation
