Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity
Abstract
Close to the origin, the nonlinear Klein--Gordon equations on the circle are nearly integrable Hamiltonian systems which have infinitely many almost conserved quantities called harmonic actions or super-actions. We prove that, at low regularity and with a CFL number of size 1, this property is preserved if we discretize the nonlinear Klein--Gordon equations with the symplectic mollified impulse methods. This extends previous results of D. Cohen, E. Hairer and C. Lubich to non-smooth solutions.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.12363
- arXiv:
- arXiv:2406.12363
- Bibcode:
- 2024arXiv240612363A
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Numerical Analysis