Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity
Analysis of PDEs
2025-05-07 v2 Numerical Analysis
Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2406.12363,
title = {Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity},
author = {Charbella Abou Khalil and Joackim Bernier},
journal= {arXiv preprint arXiv:2406.12363},
year = {2025}
}