Wave breaking for the Stochastic Camassa-Holm equation
Dan O. Crisan, Darryl D. Holm
TL;DR
This paper demonstrates that wave breaking occurs with positive probability in the Stochastic Camassa-Holm equation, indicating stochasticity does not prevent peakon formation and suggesting emergent wave trains of peakons in long-term solutions.
Contribution
It proves wave breaking occurs in SCH despite stochastic effects and conjectures the formation of stochastic peakon wave trains over time.
Findings
Wave breaking occurs with positive probability in SCH.
Stochasticity does not prevent peakon formation.
Long-term solutions may consist of stochastic wave trains.
Abstract
We show that wave breaking occurs with positive probability for the Stochastic Camassa-Holm (SCH) equation. This means that temporal stochasticity in the diffeomorphic flow map for SCH does not prevent the wave breaking process which leads to the formation of peakon solutions. We conjecture that the time-asymptotic solutions of SCH will consist of emergent wave trains of peakons moving along stochastic space-time paths.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models