Consistent Riccati expansion solvable classification and soliton-cnoidal wave interaction solutions for an extended Korteweg-de Vries equation |
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| Authors: | Wenguang Cheng Tianzhou Xu |
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| Institution: | 1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China;2. Department of Mathematics, Yuxi Normal University, Yuxi 653100, PR China |
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| Abstract: | In this paper, we consider an extended Korteweg-de Vries (KdV) equation. Using the consistent Riccati expansion (CRE) method of Lou, the extended KdV equation is proved to be CRE solvable in only two distinct cases. These two CRE solvable models are the KdV-Lax and KdV-Sawada-Kotera (KdV-SK) equations. In addition, applying the nonauto-Bäcklund transformations which are provided by the CRE method, we present the explicit construction for soliton-cnoidal wave interaction solutions which represent a soliton propagating on a cnoidal periodic wave background in the KdV-Lax and KdV-SK equations, respectively. |
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| Keywords: | Consistent Riccati expansion solvable classification Extended Korteweg-de Vries equation Soliton-cnoidal wave interaction solution |
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