Oscillatory waves in discrete scalar conservation laws. (English) Zbl 1261.65088
Author’s abstract: We study Hamiltonian difference schemes for scalar conservation laws with monotone flux function and establish the existence of of a three-parameter family of periodic traveling waves (wavetrains). The proof is based on an integral equation for the dual wave profile and employs constrained maximization as well as the invariance properties of a gradient flow. We also discuss the approximation of wavetrains and present some numerical results.
Reviewer: Fozi Dannan (Damascus)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
Keywords:
conservation laws; dispersive shocks; Hamiltonian lattices; variational integrators; Hamiltonian difference schemes; periodic traveling waves (wavetrains); numerical resultsReferences:
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