2017 Volume 7 Issue 3
Article Contents

Jing Li, Xin Li, Wei Zhang. RESEARCH ON TRAVELING WAVE SOLUTIONS FOR A CLASS OF (3+1)-DIMENSIONAL NONLINEAR EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 841-856. doi: 10.11948/2017053
Citation: Jing Li, Xin Li, Wei Zhang. RESEARCH ON TRAVELING WAVE SOLUTIONS FOR A CLASS OF (3+1)-DIMENSIONAL NONLINEAR EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 841-856. doi: 10.11948/2017053

RESEARCH ON TRAVELING WAVE SOLUTIONS FOR A CLASS OF (3+1)-DIMENSIONAL NONLINEAR EQUATION

  • Fund Project:
  • Nonlinear wave phenomena are of great importance in the nature, and have became for a long time a challenging research topic for both pure and applied mathematicians. In this paper the solitary wave, kink (anti-kink) wave and periodic wave solutions for a class of (3+1)-dimensional nonlinear equation were obtained by some effective methods from the dynamical systems theory.
    MSC: 34C37;35Q51
  • 加载中
  • [1] A. M Abourabia and A. M Morad, Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter, Physica A, 2015, 437, 333-350.

    Google Scholar

    [2] M. Alquran and A. Qawasmeh, Soliton solutions of shallow water wave equations by means of G'/G expansion method, J. Appl. Anal. Comput., 2014, 4(3), 221-229.

    Google Scholar

    [3] X. Geng, C. Cao and H. Dai, Quasi-periodic solutions for some (2+1)-dimensional integrable models generated by the Jaulent-Miodek hierarchy, Journal of Physics A-Mathematical and General, 2001, 34(5), 989-1004.

    Google Scholar

    [4] X. Geng and Y. Ma, N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation, Phys. Lett. A, 2007, 369(4), 285-289.

    Google Scholar

    [5] W. Hereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Math. Comput. Simulation, 1997, 43(1), 13-27.

    Google Scholar

    [6] R. Hirota, The direct method in soliton theory, Cambridge University Press, Cambridge, 2004.

    Google Scholar

    [7] J. Li and F. Chen, Exact travelling wave solutions and their dynamical behavior for a class coupled nonlinear wave equations, Discrete Cont. Dyn. Sys., Series B, 2013, 18(1), 163-172.

    Google Scholar

    [8] J. Li and G. Chen, On a class of singular nonlinear traveling wave equations, Int. J. Bifur. Chaos, 2007, 17(11), 4049-4065.

    Google Scholar

    [9] J. Li and T. He, Exact traveling wave solutions and bifurcations in a nonlinear elastic rod equation, Acta Math. Appl. Sin., English Seris, 2010, 26(2), 283-306.

    Google Scholar

    [10] X. Li, J. Han and F. Wang, The extended Riccati equation method for traveling wave solutions of ZK equation, J. Appl. Anal. Comput., 2012, 2(4), 423-430.

    Google Scholar

    [11] G. Lin, Traveling wave solutions for integro-difference systems, J. Differential Equations, 2015, 258, 2908-2940.

    Google Scholar

    [12] A. Qawasmeh and M. Alquran, Soliton and Periodic Solutions for (2+1)-Dimensional Dispersive Long Water-Wave System, Appl. Math. Sci., 2014, 8(50), 2455-2463.

    Google Scholar

    [13] T. Rehman, G. Gambino and S. Roy Choudhury, Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations, Commun. Nonlinear Sci. Numer. Simul., 2014, 19, 1746-1769.

    Google Scholar

    [14] A. M Wazwaz, Multiple kink solutions and multiple singular kink solutions for (2+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy, Phys. Lett. A, 2009, 373(21), 1844-1846.

    Google Scholar

    [15] A. M Wazwaz, Multiple soliton solutions for some (3+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy, Appl. Math. Lett., 2012, 25, 1936-1940.

    Google Scholar

    [16] J. Wu, N-soliton solution, generalized double Wronskian determinant solution and rational solution for a (2+1)-dimensional nonlinear evolution equation, Phys. Lett. A, 2008, 373(1), 83-88.

    Google Scholar

    [17] K. Zhang and J. Han, Bifurcations of traveling wave solutions for the (2+1)-dimensional generalized asymmetric Nizhnik-Novikov-Veselov equation, Appl. Math. Comput., 2015, 251, 108-117.

    Google Scholar

    [18] Z. Zhang, T. Ding, W. Huang and Z. Dong, Qualitative theory of differential equations, Science Press, Beijing, 1985.

    Google Scholar

    [19] G. Zhao and S. Ruan, Time periodic traveling wave solutions for periodic advection-reaction-diffusion systems, J. Differential Equations, 2014, 257, 1078-1147.

    Google Scholar

Article Metrics

Article views(2811) PDF downloads(885) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint