On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation

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• 作者：Xiu-Bin Wang^a ; Shou-Fu Tian ; ^a ; ^b ; ^{sftian@cumt.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{shoufu2006@126.com" class="auth_mail" title="E-mail the corresponding author} ; Mei-Juan Xua^a ; Tian-Tian Zhang^a ; ^{ttzhang@cumt.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：A (3+1)-dimensional generalized KdV-like model equation ; Bell polynomial ; Bä ; cklund transformation ; Lax pairs ; Soliton solution ; Periodic wave solution
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：20 June 2016
• 年：2016
• 卷：283
• 期：Complete
• 页码：216-233
• 全文大小：3516 K

文摘

Under investigation in this paper is the integrability of a (3+1)-dimensional generalized KdV-like model equation, which can be reduced to several integrable equations. With help of Bell polynomials, an effective method is presented to succinctly derive the bilinear formalism of the equation, based on which, the soliton solutions and periodic wave solutions are also constructed by using Riemann theta function. Furthermore, the Bäcklund transformation, Lax pairs, and infinite conservation laws of the equation can easily be derived, respectively. Finally, the relationship between periodic wave solutions and soliton solutions are systematically established. It is straightforward to verify that these periodic waves tend to soliton solutions under a small amplitude limit.