Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 266, Issue 4, Pages 1946-1968Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.08.017
Keywords
Traveling waves; Instability; Modified Camassa-Holm equation
Categories
Funding
- FAPESP (Fundacao de Amparo a Pesquisa do Estado de Sao Paulo - Brazil) [2017/23751-2]
- CAPES (Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior - Brazil)
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This paper is concerned with the orbital instability for a specific class of periodic traveling wave solutions with the mean zero property and large spatial period related to the modified Camassa-Holm equation. These solutions, called snoidal waves, are written in terms of the Jacobi elliptic functions. To prove our result we use the abstract method of Grillakis, Shatah and Strauss [23], the Floquet theory for periodic eigenvalue problems and the n-gaps potentials theory of Dubrovin, Matveev and Novikov [19]. (C) 2018 Elsevier Inc. All rights reserved.
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