---

Discontinuity, Nonlinearity, and Complexity 1(2) (2012) 161--170 | DOI:10.5890/DNC.2012.05.001

Abdul-MajidWazwaz

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

Download Full Text PDF

 

Abstract

In this work, we derive one kink solution for each equation of a variety of nonlinear fifth-order equations. Each equation involves a third order temporal derivative and a mixed fifth-order derivative. The simplified form of Hirota’s method will be used to derive these solutions. The proposed work presents reliable approach compared to some existing techniques.

References

1. [1]	Wazwaz, A.M. (2011), A new fifth-order nonlinear integrable equation: multiple soliton solutions,Phys. Scr., 83, 015012.

2. [2]	Wazwaz, A.M. (2011), A new generalized fifth-order nonlinear integrable equation,Phys. Scr., 83, 035003.

3. [3]	Hirota, R. (2004), The Direct Method in Soliton Theory, Cambridge University Press, Cambridge.

4. [4]	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.

5. [5]	Hereman,W. (2006), Symbolic Computation of Conservation Laws of Nonlinear Partial Differential Equations in Multi-dimensions,International Journal of Quantum Chemistry, 106 (1), 278-299.

6. [6]	Triki, H., Wazwaz, A.M. (2009), Sub-ODE method and soliton solutions for the variable- coefficient mKdV equation, Appl. Math. Comput., 214, 370-373.

7. [7]	Triki, H., Wazwaz, A.M. (2009), Bright and dark soliton solutions for a K(m,n) equation with t-dependent coefficients, Phys. Lett A, 373, 2162-2215.

8. [8]	Dehghan, M. and Shokri, A.(2008),A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions,Comput.Math. Simulation, 79, 700-715.

9. [9]	Dehghan, M. and Ghesmati, A.(2010), Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM), Comput. Phys. Commun., 181, 772-786.

10. [10]	Wazwaz, A.M. (2009), Partial Differential Equations and Solitary Waves Theorem, Springer and HEP, Berlin and Beijing.

11. [11]	Wazwaz, A.M. (2010), Multiple soliton solutions for coupled KdV and coupled KP Systems, Canadian Journal of Physics, 87( 12), 1227-1232 .

12. [12]	Wazwaz, A.M. (2010), Multiple soliton solutions for the (2+1)-dimensional asymmetric Nizhanik-Novikov- Veselov equation, Nonlinear Analysis Series A: Theory, Methods & Applications, 72, 1314-1318.

13. [13]	Wazwaz, A.M. (2010), The (2+1) and (3+1)-dimensional CBS equation: multiple soliton solutions and multiple singular soliton solutions, Multiple, Zeitschrift fur Naturforschung A (ZNA), 65a, 173-181.

14. [14]	Wazwaz, A.M. (2007),Multiple-front solutions for the Burgers equation and the coupled Burgers equations, Appl. Math. Comput., 190, 1198-1206.

15. [15]	Wazwaz, A.M. (2007), New solitons and kink solutions for the Gardner equation, Communications in Nonlinear Science and Numerical Simulation, 12(8), 1395-1404.

16. [16]	Wazwaz, A.M. (2007), Multiple-soliton solutions for the Boussinesq equation, Appl. Math. Comput., 192, 479- 486.

17. [17]	Wazwaz, A.M. (2008), The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation,Appl.Math. Comput., 199(1), 133-138.

18. [18]	Wazwaz, A.M. (2008), The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves, Appl. Math. Comput., 201(1/2), 489-503.

19. [19]	Wazwaz, A.M. (2008), Solitons and singular solitons for the Gardner-KP equation, Appl. Math. Comput., 204(1), 162-169.

20. [20]	Wazwaz, A.M. (2009),Multiple kink solutions and multiple singular kink solutions for (2+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy, Phys. Lett. A, 373, 1844-1846.