A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908456000159744 |
|---|---|
| author | Holm, Darryl D. Singh, Maneesh Kumar Street, Oliver D. |
| author_facet | Holm, Darryl D. Singh, Maneesh Kumar Street, Oliver D. |
| contents | We introduce a stochastic perturbation of the Camassa-Holm equation such that, unlike previous formulations, energy is conserved by the stochastic flow. We compare this to a complementary approach which preserves Casimirs of the Poisson bracket. Through an energy preserving numerical implementation of the model, we study the influence of noise on the well-known 'peakon' formation behaviour of the solution. The energy conserving stochastic approach generates an ensemble of solutions which are spread around the deterministic Camassa-Holm solution, whereas the Casimir conserving alternative develops peakons which may propagate away from the deterministic solution more dramatically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations Holm, Darryl D. Singh, Maneesh Kumar Street, Oliver D. Statistical Mechanics Exactly Solvable and Integrable Systems 70L10 We introduce a stochastic perturbation of the Camassa-Holm equation such that, unlike previous formulations, energy is conserved by the stochastic flow. We compare this to a complementary approach which preserves Casimirs of the Poisson bracket. Through an energy preserving numerical implementation of the model, we study the influence of noise on the well-known 'peakon' formation behaviour of the solution. The energy conserving stochastic approach generates an ensemble of solutions which are spread around the deterministic Camassa-Holm solution, whereas the Casimir conserving alternative develops peakons which may propagate away from the deterministic solution more dramatically. |
| title | A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations |
| topic | Statistical Mechanics Exactly Solvable and Integrable Systems 70L10 |
| url | https://arxiv.org/abs/2507.14264 |