Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity
<|reference_start|>Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity: 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.<|reference_end|>
@article{khalil2024almost,
    title={Almost conservation of the harmonic actions for fully discretized
  nonlinear Klein--Gordon equations at low regularity},
    author={Charbella Abou Khalil (Nantes Univ), Joackim Bernier (Nantes Univ)},
    journal={arXiv preprint arXiv:2406.12363},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.12363},
    primaryClass={math.AP cs.NA math.NA}
}