Bäcklund transformation classification, integrability and exact solutions to the generalized Burgers’–KdV equation

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• 作者：Hanze Liu ; ^a ; ^b ; ^{hanze_liu@126.com" class="auth_mail" title="E-mail the corresponding author} ; Xiangpeng Xin^a ; Zenggui Wang^a ; Xiqiang Liu^a
• 关键词：Direct method ; Homogeneous balance principle ; Bä ; cklund transformation ; Integrability ; Exact solution
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：44
• 期：Complete
• 页码：11-18
• 全文大小：400 K

文摘

This paper is concerned with the Bäcklund transformations (BTs) of the nonlinear evolution equations (NLEEs). Based on the homogeneous balance principle (HBP), the existence of the BT of the generalized Burgers’–KdV (B–KdV) equation is classified, then the BTs of the nonlinear equations are given. In general, the method can be used to construct BTs of the nonlinear evolution equations in polynomial form. Furthermore, the integrability and exact explicit solutions to the nonlinear equations are investigated.