Share This Article:

The Periodic Solitary Wave Solutions for the (2 + 1)-Dimensional Fifth-Order KdV Equation

Abstract Full-Text HTML XML Download Download as PDF (Size:886KB) PP. 639-643
DOI: 10.4236/jamp.2014.27070    2,804 Downloads   3,686 Views   Citations
Author(s)    Leave a comment


The (2 + 1)-dimensional fifth-order KdV equation is an important higher-dimensional and higher-order extension of the famous KdV equation in fluid dynamics. In this paper, by constructing new test functions, we investigate the periodic solitary wave solutions for the (2 + 1)-dimensional fifth-order KdV equation by virtue of the Hirota bilinear form. Several novel analytic solutions for such a model are obtained and verified with the help of symbolic computation.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Meng, X. (2014) The Periodic Solitary Wave Solutions for the (2 + 1)-Dimensional Fifth-Order KdV Equation. Journal of Applied Mathematics and Physics, 2, 639-643. doi: 10.4236/jamp.2014.27070.


[1] Ablowitz, M.J. and Clarkson, P.A. (1991) Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, New York.
[2] Osborne, A.R. (2010) Nonlinear Ocean Waves and the Inverse Scattering Transform. Academic Press, San Diego.
[3] Gu, C.H., Hu, H.S. and Zhou, Z.X. (1999) Darboux Transformation in Soliton Theory and Its Geometric Applications. Shanghai Scientific Techinical Publishers, Shanghai.
[4] Lou, S.Y. and Chen, L.L. (1999) Formally Variable Separation Approach for Nonintegrable Models. Journal of Mathematical Physics, 40, 6491-6500.
[5] Ma, W.X., Abdeljabbar, A. and Asaad, M.G. (2011) Wronskian and Grammian Solutions to a (3 + 1)-Dimensional Generalized KP Equation. Applied Mathematics and Computation, 217, 10016-10023.
[6] Hu, X.B., Zhao, J.X. and Tam, H.W. (2004) Pfaffianization of the Two-Dimensional Toda Lattice. Journal of Mathematical Analysis and Applications, 296, 256-261.
[7] Qu, C.Z. (2006) Symmetries and Solutions to the Thin Film Equations. Journal of Mathematical Analysis and Applications, 317, 381-397.
[8] Dai, Z.D., Liu, Z.J. and Li, D.L. (2008) Exact Periodic Solitary-Wave Solution for KdV Equation. Chinese Physics Letters, 25, 1531-1533.
[9] Xu, X.G., Meng, X.H., Zhang, C.Y. and Gao, Y.T. (2013) Analytical Investigation of the Caudrey-Dodd-Gibbon-Kotera-Sawada Equation Using Symbolic Computation. International Journal of Modern Physics B, 27, Article ID: 1250124.
[10] Konopelchenko, B. and Dubrovsky, V. (1984) Some New Integrable Nonlinear Evolution Equations in 2 + 1 Dimensional. Physics Letters A, 102, 15-17.
[11] Cheng, Y. and Li, Y.S. (1992) Constraints of the 2 + 1 Dimensional Integrable Soliton Systems. Journal of Physics A: Mathematical and General, 25, 419-431.
[12] Cao, C.W., Wu, Y.T. and Geng, X.G. (1999) On Quasi-Periodic Solutions of the 2 + 1 Dimensional Caudrey-DoddGibbon-Kotera-Sawada Equation. Physics Letters A, 256, 59-65.
[13] Lv, N., Mei, J.Q. and Zhang, H.Q. (2010) Symmetry Reductions and Group-Invariant Solutions of (2 + 1)-Dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada Equation. Communications in Theoretical Physics, 53, 591-595.
[14] Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press, Cambridge.

comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.