Back
 JAMP  Vol.2 No.3 , February 2014
Similarity Reduction of Nonlinear Partial Differential Equations
Abstract: In this work, the HB method is extended to search for similarity reduction of nonlinear partial differential equations. This method is generalized and will apply for a (2 + 1)-dimensional higher order Broer-Kaup System. Some new exact solutions of Broer-Kaup System are found.
Cite this paper: Al-Johani, A. (2014) Similarity Reduction of Nonlinear Partial Differential Equations. Journal of Applied Mathematics and Physics, 2, 22-32. doi: 10.4236/jamp.2014.23003.
References

[1]   H. A. Zedan, “Exact Solutions for the Generalized KdV Equation by Using Backlund Transformations,” Journal of the Franklin Institute, Vol. 348, No. 8, 2011, pp. 1751-1768. http://dx.doi.org/10.1016/j.jfranklin.2011.04.013

[2]   D.-S. Li, et al., “Solving the (2 + 1)-Dimensional Higher Order Broer-Kaup System via a Transformation and Tanh-Function mEthod,” Chaos, Solitons & Fractals, Vol. 20, No. 5, 2004, pp. 1021-1025. http://dx.doi.org/10.1016/j.chaos.2003.09.006

[3]   J. Mei, et al., “New Soliton-Like and Periodic Solution of (2 + 1)-Dimensional Higher Order Broer-Kaup System,” Chaos, Solitons & Fractals, Vol. 22, No. 3, 2004, pp. 669-674. http://dx.doi.org/10.1016/j.chaos.2004.02.023

[4]   D.-S. Li, et al., “Some New Types of Multisoliton Solutions for the (2 + 1)-Dimensional Higher-Order Broer-Kaup System,” Applied Mathematics and Computation, Vol. 152, No. 3, 2004, pp. 847-853. http://dx.doi.org/10.1016/S0096-3003(03)00601-5

[5]   E. G. Fan and H. Q. Zhang, “A Note on the Homogeneous Balance Method,” Physics Letters A, Vol. 246, No. 5, 1998, pp. 403-406.

[6]   E. G. Fan, “Two New Applications of the Homogeneous Balance Method,” Physics Letters A, Vol. 265, No. 5-6, 2000, pp. 353-357. http://dx.doi.org/10.1016/S0375-9601(00)00010-4

[7]   G. Bluman, “Symmetries and Differential Equations,” Springer-Verlag, New York, 1989. http://dx.doi.org/10.1007/978-1-4757-4307-4

[8]   P. J. Olver, “Applications of Lie Group to Differential Equation,” Springer-Verlag, New York, 1986. http://dx.doi.org/10.1007/978-1-4684-0274-2

[9]   P. A. Clarkson, “New Similarity Solutions for the Modified Boussinesq Equation,” Journal of Physics A: Mathematical and General, Vol. 22, No. 13, 1989, pp. 2355-2365. http://dx.doi.org/10.1088/0305-4470/22/13/029

[10]   Y. Yu, Q. Wang and H. Q. Zhang, “The Extended Jacobi Elliptic Function Method to Solve a Generalized Hirota-Satsuma Coupled KdV Equations,” Chaos, Solitons & Fractals, Vol. 26, No. 5, 2005, pp. 1415-1421. http://dx.doi.org/10.1016/j.chaos.2005.04.011

[11]   J. L. Zhang, M. L. Wang, Y. M. Wang, Z. D. Fang, “The Improved F-Expansion Method and Its Applications,” Physics Letters A, Vol. 350, No. 1-2, 2006, pp. 103-109. http://dx.doi.org/10.1016/j.physleta.2005.10.099

[12]   E. M. E. Zayed and H. Zedan, “On the Solitary Wave Solutions for Nonlinear Hirota-Satsuma Coupled KdV of Equations,” Chaos, Solitons & Fractals, Vol. 22, No. 2, 2004, pp. 285-303. http://dx.doi.org/10.1016/j.chaos.2003.12.045

[13]   A. M. Wadati, “Introduction to Solitons,” Pramana: Journal of Physics, Vol. 57, No. 5-6, 2001, pp. 841-847.

[14]   Z. Chen, D. H. Zhao and J. Ruan, “Dynamic Analysis of High-Order Cohen-Grossberg Neural Networks with Time Delay,” Chaos, Solitons & Fractals, Vol. 32, No. 4, 2007, pp. 1538-1546. http://dx.doi.org/10.1016/j.chaos.2005.11.095

[15]   Hassan A. Zedan, “Solution of (3 + 1) - Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method,” Mathematical Problems in Engineering, Vol. 2012, 2012, 14 p.

 
 
Top