Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916720939106304 |
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| author | Khalil, Charbella Abou Bernier, Joackim |
| author_facet | Khalil, Charbella Abou Bernier, Joackim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity Khalil, Charbella Abou Bernier, Joackim Analysis of PDEs Numerical Analysis 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. |
| title | Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2406.12363 |