Research ArticleOpen AccessGoogle Scholar indexed
New Periodic Solitary Wave Solutions for a Variable-Coefficient Gardner Equation from Fluid Dynamics and Plasma Physics
- 1
Applied Mathematics·Volume 01 (2010)·Pages 307–311·Published 29 October 2010·DOI10.4236/am.2010.14040
Copy link · social · email
Abstract
The Gardner equation with a variable-coefficient from fluid dynamics and plasma physics is investigated. Different kinds of solutions including breather-type soliton and two soliton solutions are obtained using bilinear method and extended homoclinic test approach. The proposed method can also be applied to solve other types of higher dimensional integrable and non-integrable systems.
KeywordsExtended Homoclinic Test ApproachBilinear FormGardner Equation with a Variable-CoefficientPeriodic Solitary Wave Solutions
- M. Ablowitz and P. A. Clarkson, “Soliton, Nonlinear Evolution Equations and Inverse Scattering,” Cambridge University Press, New York, 1991.
- S. A. El-Wakil and M. A. Abdou, “New Applications of Adomian Decomposition Method,” Chaos, Solitons and Fractals, Vol. 33, No. 2, 2007, pp. 513-522.
- S. A. El-Wakil and M. A. Abdou, “New Exact Travelling Wave Solutions of Two Nonlinear Physical Models,” Nonlinear Analysis, Vol. 68, No. 2, 2008, pp. 235-245.
- J.-H. He and M. A. Abdou, “New Periodic Solutions for Nonlinear Evolution Equations Using Exp Function Method,” Chaos, Solitons and Fractals, Vol. 34, No. 5, 2007, pp. 1421-1429.
- M. A. Abdou and S. Zhang, “New Periodic Wave Solutions via Extended Mapping Method,” Communication in Nonlinear Science and Numerical Simulation, Vol. 14, No. 1, 2009, pp. 2-11.
- M. A. Abdou, “On the Variational Iteration Method,” Physics Letters A, Vol. 366, No. 1-2, 2007, pp. 61-68.
- R. Hirota, “Direct Method in Soliton Theory,” In: R. K. Bullough and P. J. Caudrey, Ed., Solitons, Springer, Berlin, 1980, pp. 1-196.
- M. A. Abdou, “Generalized Solitary and Periodic Solutions for Nonlinear Partial Differential Equations by the Exp-Function Method,” Journal of Nonlinear Dynamics, Vol. 52, No. 1-2, 2008, pp. 1-9.
- G. M. Wei, Y. T. Gao and X. G. Xu, “Painlevé Analysis and Transformations for a Generalized Two-Dimensional Variable-Coefficient Burgers Model from Fluid Mechanics, Acoustics and Cosmic-Ray Astrophysics,” Nuovo Cimento B, Vol. 121, No. 4, 2006, pp. 327-342.
- P. E. P. Holloway, E. Pelinovsky, T. Talipova and B. Barnes, “A Nonlinear Model of Internal Tide Transformation on the Australian North West Shelf,” Journal of Physical Oceanography, Vol. 27, No. 6, 1997, pp. 871- 896.
- J. A. Gear and R. Grimshaw, “A Second-Order Theory for Solitary Waves in Shallow Fluids,” Physics of Fluid, Vol. 26, No. 14, 1983, 16 pages.
- S. Watanabe, “Ion Acoustic Soliton in Plasma with Negative Ion,” Journal of Physical Society of Japan, Vol. 53, 1984, pp. 950-956.
- X.-G. Xu, X. Meng, Y. Gao and X. Wen, “Analytic N- Solitary-Wave Solution of a Variable-Coefficient Gardner Equation from Fluid Dynamics and Plasma Physics,” Applied Mathematics and Computation, Vol. 210, No. 2, 2009, pp. 313-320.
- N. Joshi, “Painlevé Property of General Variable- Coefficient Versions of the Korteweg-De Vries and Non-Linear Schr?dinger Equations,” Physics Letter A, Vol. 125, No. 9, 1987, p. 456.