Quasi-periodic wave solutions and two-wave solutions of the KdV–Sawada–Kotera–Ramani equation

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• 作者：Lijun Zhang ; Chaudry Masood Khalique
• 关键词：The KdV–Sawada–Kotera–Ramani equation ; Two ; wave solutions ; Quasi ; periodic solutions
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：87
• 期：3
• 页码：1985-1993
• 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

The two-wave solutions of the KdV–Sawada–Kotera–Ramani equation are studied in this paper. By reducing this high-order wave equation into two associated solvable ordinary differential equations, we derive the two-wave solutions in the form \(u(x,t)=U(x-c_1t)+V(x-c_2t)\) which includes solitary wave solutions, periodic solutions and quasi-periodic wave solutions by letting \(c_1=c_2\). We obtain a family of new exact two-wave solutions combined by a solitary wave and a periodic wave with two different wave speeds. These new exact two-wave solutions are neither periodic nor quasi-periodic wave solutions but approximating periodic wave solutions as time tends to infinity. The process of translation of the two-wave solution combined by two solitary wave solutions is illustrated by simulation. The approach presented in this work might be applied to study the bifurcation of multi-wave solutions of some important high-order nonlinear wave model equations.