The Riemann–Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient ( \(\varvec{2+1}\) )-dimensional KdV equation

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• 作者：Zhonglong Zhao ; Bo Han
• 关键词：A generalized variable coefficient (\(2+1\) ; ) ; dimensional Korteweg–de Vries equation ; Bäcklund transformation ; Soliton solutions ; Quasiperiodic wave solutions
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：87
• 期：4
• 页码：2661-2676
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

In this paper, the Riemann–Bäcklund method is extended to a generalized variable coefficient (\(2+1\))-dimensional Korteweg–de Vries equation. The soliton and quasiperiodic wave solutions are investigated systematically. The relations between the quasiperiodic wave solutions and the soliton solutions are rigorously established by a limiting procedure. It is proved that the periodic wave solutions tend to the soliton solutions under a small amplitude limit. Furthermore, the propagation characteristics of the soliton solutions and periodic wave solutions are discussed through the graphical analysis.