---

Journal of Applied Nonlinear Dynamics 2(1) (2012) 95--102 | DOI:10.5890/JAND.2012.09.007

Abdul-Majid Wazwaz

Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

Download Full Text PDF

 

Abstract

In this work, we investigate the (2+1)-dimensional third-order and fourth-order Sharma–Tasso–Olver (STO) equations. Moreover, we also study the (2+1)-dimensional generalized Sharma– Tasso–Olver-Burgers (STO-B) equation. Multiple kink solutions are formally derived for each equation. The Hereman-Nuseir method, a simplified form of Hirota’s direct method is applied to carry out this analysis.

References

1. [1]	Tasso, H. (1976), Cole ansatz and extension of Burgers equation, Report IPP6/142 Ber. MPI fur Plasmaphysik (Garching).

2. [2]	Sharma, A.S., Tasso, H. (1977), Connection between wave envelope and explicit solution of a nonlinear dispersive equation, Report IPP6/158 Ber. MPI fur Plasmaphysik (Garching), 1-10.

3. [3]	Olver, P.J. (1977), Evolution equation possessing infinite many symmetries, Journal of Mathematical Physics, 18 (6), 1212-1215.

4. [4]	Wazwaz, A.M. (2007), New solitons and kinks solutions to the Sharma-Tasso-Olver equation,Applied Mathematics and Computation , 188, 1205-1213.

5. [5]	Yan, Z. (2003), Integrability of two types of (2+1)-dimensional generalized Sharma-Tasso-Olver integrodifferential equations, MM Research Preprints, 22, 302-324.

6. [6]	Wang, S., Tang, X., and Lou, S.Y. (2004), Soliton fission and fusion: Burgers equation and Sharma- Tasso-Olver equation, Chaos, Solitons & Fractals, 21, 231-239.

7. [7]	Hirota, R. (2004), The Direct Method in Soliton Theory, Cambridge University Press, Cambridge.

8. [8]	Hereman, W. and Nuseir, A. (1997), Symbolic methods to construct exact solutions of nonlinear partial differential equations, Mathematics and Computers in Simulation, 43, 13-27.

9. [9]	Biswas, Anjan (2008), 1-soliton solution of (1+2) dimensional nonlinear Schrödinger's equation in dualpower law media, Physics Letters A, 372, 5941-5943.

10. [10]	Dehghan, M. and Shokri, A. (2008), A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions,Mathematics and Computers in Simulation , 79, 700-715.

11. [11]	Wazwaz, A.M. (2009), Partial Differential Equations and Solitary Waves Theorem, Springer and HEP, Berlin and Beijing.

12. [12]	Wazwaz, A.M. (2011), Linear and Nonlinear Integral Equations, Springer and HEP, Berlin and Beijing.

13. [13]	Wazwaz, A.M.(2011), A new (2+1)-dimensional KdV equation and its extension to a new (3+1)- dimensional KP equation, Physica Scripta, 84, 035010.

14. [14]	Wazwaz, A.M. (2011), Multiple kink solutions for the (3+1) dimensional Burgers hierarchy, Physica Scripta, 84, 035001.

15. [15]	Wazwaz, A.M. (2011), Multiple-front waves for extended form of modified Kadomtsev-Petviashvili equation, Applied Mathematics and Mechanics, 32(7), 875-880.

16. [16]	Wazwaz, A.M. (2011), Integrability of two coupled KP equations, Pramana Journal of Physics, 77(2), 233-242 .

17. [17]	Wazwaz, A.M. (2011), Multiple soliton solutions for (2+1)-dimensional Sawada-Kotera and Caudrey- Dodd-Gibbon equations, Mathematical Methods in the Applied Sciences, 34, 1580-1586.

18. [18]	Wazwaz, A.M. (2011),Soliton solutions for seventh-order Kawahara equation with time dependent coefficients, Modern Physics Letters B, 25(9), 643-648 .

19. [19]	Wazwaz, A.M. (2009), Multiple kink solutions and multiple singular kink solutions for two systems of coupled Burgers' type equations, Communications in Nonlinear Science and Numerical Simulations, 14, 2962-2970.