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Cusped and Smooth Solitons for the Generalized Camassa‐Holm Equation on the Nonzero Constant Pedestal

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  • Dong Li
  • Yongan Xie
  • Shengqiang Tang

Abstract

We investigate the traveling solitary wave solutions of the generalized Camassa‐Holm equation ut − uxxt + 3u2ux = 2uxuxx + uuxxx on the nonzero constant pedestal limξ→±∞⁡u(ξ) = A. Our procedure shows that the generalized Camassa‐Holm equation with nonzero constant boundary has cusped and smooth soliton solutions. Mathematical analysis and numerical simulations are provided for these traveling soliton solutions of the generalized Camassa‐Holm equation. Some exact explicit solutions are obtained. We show some graphs to explain our these solutions.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:423063
DOI: 10.1155/2014/423063
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