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Solitary waves for a nonlinear dispersive long wave equation

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Abstract

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 solitary waves may merge into a periodic wave, and its amplitude is nearly equal to the sum of the amplitudes of the two solitary wave solutions.

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Authors and Affiliations

  1. Faculty of Science, Jiangsu University, Zhenjiang, 212013, China

    Zhengdi Zhang & Qinsheng Bi

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  1. Zhengdi Zhang
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  2. Qinsheng Bi
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Correspondence to Qinsheng Bi.

Additional information

The project supported by the National Natural Science Foundation of China (10602020).

The English text was polished by Yunming Chen.

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Zhang, Z., Bi, Q. Solitary waves for a nonlinear dispersive long wave equation. Acta Mech Sin 24, 455–462 (2008). https://doi.org/10.1007/s10409-008-0157-y

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  • DOI: https://doi.org/10.1007/s10409-008-0157-y

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