Solitary waves for a nonlinear dispersive long wave equation

• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2008,（4）
• 页码范围: 455-462
• 页数: 8页
• 语种: 英文
• DOI: 10.1007/s10409-008-0157-y

摘要

All the possible traveling wave solutions of Whitham-Broer-Kaup (WBK) equation are investigated in the present paper. By employing phase plane analysis, transition boundaries are derived to divide the parameter space into several regions associated with different types of phase portraits corresponding to different forms of wave solutions. All the exact expressions of bounded wave solutions are obtained as well as their existence conditions. The mechanism of bifurcation between different waves with varying Hamiltonian value has been revealed. It is pointed out that as the periods of two coexisted periodic waves tend to infinity, they may evolve to two solitary waves. Furthermore, when their trajectories pass through the common saddle point, the two solitarywavesmay merge into a periodicwave, and its amplitude is nearly equal to the sum of the amplitudes of the two solitary wave solutions.