Solitary waves for a nonlinear dispersive long wave equation
作者： Zhengdi Zhang , Qinsheng Bi
DOI: 10.1007/S10409-008-0157-Y
关键词:
摘要: All the possible traveling wave solutions of Whitham–Broer–Kaup (WBK) equation are investigated in present paper. By employing phase plane analysis, transition boundaries derived to divide parameter space into several regions associated with different types portraits corresponding forms solutions. exact expressions bounded obtained as well their existence conditions. The mechanism bifurcation between waves varying Hamiltonian value has been revealed. It is pointed out that periods two coexisted periodic tend infinity, they may evolve solitary waves. Furthermore, when trajectories pass through common saddle point, merge a wave, and its amplitude nearly equal sum amplitudes
springer.com
harvard.edu
sci-hub.se 参考文章(23)
Zhengdi Zhang, Qinsheng Bi, Bifurcations of a Generalized Camassa-Holm Equation International Journal of Nonlinear Sciences and Numerical Simulation. ,vol. 6, pp. 81- 86 ,(2005) , 10.1515/IJNSNS.2005.6.1.81
A.H.A. Ali, A.A. Soliman, K.R. Raslan, Soliton solution for nonlinear partial differential equations by cosine-function method Physics Letters A. ,vol. 368, pp. 299- 304 ,(2007) , 10.1016/J.PHYSLETA.2007.04.017
Antonio Degasperis, Sara Lombardo, Exact solutions of the 3-wave resonant interaction equation Physica D: Nonlinear Phenomena. ,vol. 214, pp. 157- 168 ,(2006) , 10.1016/J.PHYSD.2006.01.003
Ranchao Wu, Jianhua Sun, Soliton-like solutions to the GKdV equation by extended mapping method Chaos Solitons & Fractals. ,vol. 31, pp. 70- 74 ,(2007) , 10.1016/J.CHAOS.2005.09.032
Emmanuel Yomba, Yan-ze Peng, Fission, fusion and annihilation in the interaction of localized structures for the (2+1)-dimensional generalized Broer–Kaup system Chaos, Solitons & Fractals. ,vol. 28, pp. 650- 667 ,(2006) , 10.1016/J.CHAOS.2005.08.007
Lijun Zhang, Jibin Li, Bifurcations of traveling wave solutions in a coupled non-linear wave equation Chaos Solitons & Fractals. ,vol. 17, pp. 941- 950 ,(2003) , 10.1016/S0960-0779(02)00442-3
T. Alagesan, Y. Chung, K. Nakkeeran, Bäcklund transformation and soliton solutions for the coupled dispersionless equations Chaos Solitons & Fractals. ,vol. 21, pp. 63- 67 ,(2004) , 10.1016/S0960-0779(03)00186-3
Zhenya Yan, Hongqing Zhang, New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water Physics Letters A. ,vol. 285, pp. 355- 362 ,(2001) , 10.1016/S0375-9601(01)00376-0
SA El-Wakil, EM Abulwafa, A Elhanbaly, MA Abdou, None, The extended homogeneous balance method and its applications for a class of nonlinear evolution equations Chaos, Solitons & Fractals. ,vol. 33, pp. 1512- 1522 ,(2007) , 10.1016/J.CHAOS.2006.03.010
J. Krishnan, O. Runborg, I.G. Kevrekidis, Bifurcation analysis of nonlinear reaction¿diffusion problems using wavelet-based reduction techniques Computers & Chemical Engineering. ,vol. 28, pp. 557- 574 ,(2004) , 10.1016/J.COMPCHEMENG.2003.08.013