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Bibliographic Details
Main Authors: Holm, Darryl D., Singh, Maneesh Kumar, Street, Oliver D.
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.14264
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Table of 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.