Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 266, Issue 2, Pages 433-477Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2013.09.021
Keywords
Modified mu-Camassa-Holm equation; Integrable systems; Wave breaking; Peakons
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Funding
- NSF-China for Distinguished Young Scholars [10925104]
- PhD Programs Foundation of Ministry of Education of China [20106101110008]
- NSF-China [11001219, 11271192]
- SRP-Shaanxi grant [2010JK860]
- China Scholarship Council
- NSF [DMS-1207840]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1207840] Funding Source: National Science Foundation
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Considered herein is a modified periodic Camassa-Holm equation with cubic nonlinearity which is called the modified mu-Camassa-Holm equation. The proposed equation is shown to be formally integrable with the Lax pair and bi-Hamiltonian structure. Local well-posedness of the initial-value problem to the modified mu-Camassa-Holm equation in the Besov space is established. Existence of peaked traveling-wave solutions and formation of singularities of solutions for the equation are then investigated. It is shown that the equation admits a single peaked soliton and multi-peakon solutions with a similar character of the mu-Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and several wave-breaking mechanisms for solutions with certain initial profiles are described in detail. (C) 2013 Elsevier Inc. All rights reserved.
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