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On the stability of the solitary waves to the rotation Benjamin‐Ono equation
Author(s) -
Darwich Mohamad
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5335
Subject(s) - mathematics , uniqueness , stability (learning theory) , rotation (mathematics) , mathematical analysis , minification , wave equation , traveling wave , mathematical physics , geometry , mathematical optimization , machine learning , computer science
In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin‐Ono equation. By solving a minimization problem on the line, we construct a family of even travelling waves ψ c , γ . We then prove the uniqueness of even ground states associated with large speed and their orbital stability. Note that this improves the results in Esfahani and Levandosky, where only the stability of the set of ground states is proven.