Global existence of small-norm solutions in the reduced Ostrovsky equation

2012/10/24 by Roger Grimshaw, Grimshaw, Roger, Dmitry E. Pelinovsky +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1210.6526

11 pages; 1 figure

openalex publication_date 2012/10/24 · arxiv created 2013/04/05 · arxiv updated 2013/04/08 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitzéica equation and prove global existence of small-norm solutions in Sobolev space H³(R). This scenario is an alternative to finite-time wave breaking of large-norm solutions of the reduced Ostrovsky equation. We also discuss a sharp sufficient condition for the finite-time wave breaking.

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