On the blow-up of solutions to the integrable modified Camassa–Holm equation

2014/01/21 by Yue Liu, Peter J. Olver, Changzheng Qu +1 · 63 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Camassa–Holm equation #Fractional Differential Equations Solutions #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Nonlinear Waves and Solitons #Nonlinear system #Physics #Sign (mathematics)

paper · doi:10.1142/s0219530514500274

published in Analysis and Applications 12(04), 355-368 (World Scientific)

openalex publication_date 2014/01/21 · crossref created 2014/01/21 · crossref issued 2014/06/17 · crossref published 2014/06/17 · crossref published-online 2014/06/17 · crossref published-print 2014/07/01 · crossref deposited 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05 · crossref indexed 2026/08/05

Abstract

We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the modified integrable Camassa–Holm equation with cubic nonlinearity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.

Citations

• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Wave breaking for nonlinear nonlocal shallow water equations