Homoclinic breather wave and rational wave of BO equation and its perturbation dynamics behavior

Abstract

Abstract: A new family of periodic breather wave solutions and kink breather wave solutions of initial perturbation for the (1+1)-dimensional Benjamin-Ono（BO） equation are obtained by using the homoclinic test method with bilinear transformation of initial perturbation. Meanwhile, rational wave solutions of initial perturbation and bifurcation point of dynamics are also gained by applying quadratic function ansatz method. It shows directly some local perturbation structure of dynamics. Results show that the dynamical behavior of the equation is sensitive to initial value.

Key words: nonlinear equation, Benjamin- Ono equation, homoclinic breather wave, rational wave, dynamic perturbation

SONG Lili1, PU Zhilin1, XIAN Daquan2. Homoclinic breather wave and rational wave of BO equation and its perturbation dynamics behavior[J]. Chinese Journal of Quantum Electronics.

References

[1]Parkes E J, et al. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations[J]. Computer Physics Communications, 1996, 98(3): 283-300. [2] He Jihuan, Wu Xuhong. Exp-function method for nonlinear wave equations[J]. Chaos Solitons and Fractals, 2006, 30(3): 700-708. [3]Wang Zhenli, Liu Xiqiang. Symmetry reduction and exact solutions of generalized fourth-order dispersive equation[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2014, 31(3): 264-272 (in Chinese). [4]LI Ning, Liu Xiqiang. New explicit solutions of generalized (3+1)D higher-order KP equation[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2013, 30(4): 391-397(in Chinese). [5]Mei Jianqin, Ma Zhangyun. N-fold Darboux transformation and multi-soliton solutions for the classical BB system[J]. Applied Mathematics and Computation, 2013, 219: 6163-6169. [6]Wazwaz A M. Multiple-soliton solutions for the KP equation by Hirota’s bilinnear method and by the tanh-coth method[J]. Applied Mathematics and Computation, 2007, 190(1): 633- 640. [7]Wang Ling, Xian Daquan. Homoclinic breather-wave solutions periodic-wave solutions and kink solitary wave solutions for CDGKS equations[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2012, 29(4): 417-420(in Chinese). [8]Meng Xianghua, Xu Ruilin, et al, Auto-Backlund transformation and novel exact analytic solutions for generalized variable-coefficient BKP equation[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2014, 31(6): 663-669(in Chinese). [9]Wang Lei, Gao Yitian, et al. Solitonic interactions, Darboux transformation and double Wronskian solutions for a variable-coefficient derivative nonlinear Schrodinger equation in the inhomogeneous plasmas[J]. Nonlinear Dynamics, 2012, 67(1): 713-722. [10]Xu Bin, Liu Xiqiang. Symmetry reduction and invariable solutions of the (2+1)D Cardner equation[J]. Chinese Journal of Quantum Electronics (量子电子学报), 2009, 26(5): 531-536(in Chinese). [11]Wang Tingting, Liu Xiqiang, Yu Jinqian. Symmetries, exact solutions of and conservation laws of CDGKS equation[J]. Chinese Journal of Quantum Electronics (量子电子学报), 2011, 28(4): 385-390(in Chinese). [12]Kang Xiaorong, Xian Daquan. Symmetry reduction and new non-traveling wave solutions of (2+l)D AKNS equation[J]. Chinese Journal of Quantum Electronics (量子电子学报), 2013, 30(6):678-683(in Chinese). [13]Liu Yong, Liu Xiqiang, Wang Zhenli. Symmetries, reductions and exact solutions of (2+1)D BLMP equation[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2014, 31(5): 533-540(in Chinese). [14]Luo Dehai. On the BO equation and its generalization in the atmosphere[J]. Science in China Ser B, 1989, 32(10):1233-1245. [15]Li Ying, Wang Lireng. Initial problem for stochastic BO equation and application to biological population in estuarial areas[J]. Journal of East China Normal University (Natural Science)(华东师范大学学报:自然科学版), 2003, 2: 22-26(in Chinese). [16]Fu Zuntao, Liu Shikuo, et al. The JEFE method and periodic solutions of two kinds of nonlinear wave equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2003, 8(2): 67-75. [17]Wang Zhen, Li Desheng, et al. A method for constructing exact solutions and application to BO equation[J]. Chinese Physics, 2005, 14: 2158-2163. [18]Xu Zhenhui, Xian Daquan, Chen Hanlin. New periodic solitary-wave solutions for the BO equation[J]. Applied Mathematics and Computation, 2010, 215: 4439-4442. [19]Yang Hui. Orbital stability of solitary waves to BO equation[J]. Journal of Mathematical Study, 2006, 3(3): 240-245.