Existence of solitary waves and periodic waves for a perturbed generalized BBM equation

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• 作者：Aiyong Chen^a ; ^{aiyongchen@163.com" class="auth_mail" title="E-mail the corresponding author} ; Lina Guo^a ; Xijun Deng^b
• 关键词：34C25 ; 34C60 ; 37C27
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：261
• 期：10
• 页码：5324-5349
• 全文大小：449 K

文摘

The existence of solitary waves and periodic waves for a perturbed generalized 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 he MathML source">c₀(h)$c_0(h)$ is decreasing on he MathML source">h∈[0,1/12]$h\in [0,1/12]$ 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.