Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu


Multiple Kink Solutions for the (2+1)-dimensional Sharma—Tasso—Olver and the Sharma—Tasso—Olver—Burgers Equations

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.