期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 261, 期 10, 页码 5324-5349出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2016.08.003
关键词
BBM equation; Traveling wave; Picard-Fuchs equation; Abelian integral
类别
资金
- National Natural Science Foundation of China [11361017]
- Guangxi Natural Science Foundation [2015GXNSFBA139004]
- Innovation Project of GUET Graduate Education [2016YJCX47]
The existence of solitary waves and periodic waves for a perturbed generalised BBM equation is established by using geometric singular perturbation theory. Attention goes to perturbations of the Hamiltonian vector field with an elliptic Hamiltonian of degree four, exhibiting a cuspidal loop. It is proven that the wave speed c(0)(h) is decreasing on h is an element of [0, 1/12] by analyzing the ratio of Abelian integrals. The upper and lower bounds of the limit wave speed are given. Moreover, the relation between the wave speed and the wavelength of traveling waves is obtained. (C) 2016 Elsevier Inc. All rights reserved.
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