The modified alternative (G′/G)-expansion method for finding the exact solutions of nonlinear PDEs in mathematical physics

International Journal of Physical Sciences

Volumn 6, Issue 35, 2011, Pages 7910-7920

  Ali Akbar, M ^a,b   Ali, Norhashidah Hj Mohd ^b  

^a SCHOOL OF PHYSICS   (Malaysia)

^b UNIVERSITY OF RAJSHAHI   (Bangladesh)

Author keywords

The (G G) expansion method; The caudrey dodd gibbon equation; The drinfeld sokolov wilson equation; The nizhnik novikov vesselov equation; The riccati equation; The traveling wave solutions; The travelling regularised long wave equation

Indexed keywords

EID: 84455181489     PISSN: 19921950     EISSN: None     Source Type: Journal    
DOI: 10.5897/IJPS11.1261     Document Type: Article

References (38)

1. Abdollahzadeh M, Hosseini M, Ghanbarpour M, Shirvani H (2010). Exact travelling solutions for fifth order Caudrey-Dodd-Gibbon equation. Int. J. Appl. Math. Comput., 2(4): 81-90.
2. Abdou MA (2007). The extended tanh-method and its applications for solving nonlinear physical models. Appl. Math. Comput., 190: 988-996.
3. Ablowitz MJ, Clarkson PA (1991). Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform. Cambridge Univ. Press. Cambridge.
4. Bekir A (2008). Application of the (G′ / G) -expansion method for nonlinear evolution equations. Phys. Lett. A, 372: 3400-3406.
5. Bekir A (2009). The tanh-coth method combined with the Riccati equation for solving nonlinear equation. Chaos, Solitons Fract., 40: 1467-1474.
6. Chen Y, Wang Q (2005). Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic functions solutions to (1+1) dimensional dispersive long wave equation. Chaos, Solitons Fract., 24: 745-757.
7. Fan EG (2000). Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A, 277: 212-218.
8. Guo S, Zhou Y (2010). The extended (G′ / G) -expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations. Appl. Math. Comput., 215: 3214-3221.
9. He JH, Wu XH (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons Fract., 30: 700-708.
10. Hirota R (1971). Exact solution of the KdV equation for multiple collisions of solutions. Phys. Rev. Lett., 27: 1192-1194.
11. Jafari M, Hosseini MM, Mohyud-Din ST, Ghovatmand M (2011). Solution of the nonlinear PDAEs by variational iteration method and its applications in nanoelectronics. Int. J. Phys. Sci., 6(6): 1535-1539.
12. Jiang B, Bi Q (2010). A study on the bilinear Caudrey-Dood-Gibbon equation. Nonlinear Anal., 72: 4530-4533.
13. Jin L (2010). Application of the variational iteration method for solving the fifth order Caudrey-Dood-Gibbon equation. Int. Math. Forum., 5(66): 3259-3265.
14. Kudryashov NA (1990). Exact solutions of the generalized Kuramoto- Sivashinsky equation. Phys. Lett. A, 147: 287-291.
15. Kudryashov NA (1991). On types of nonlinear nonintegrable equations with exact solutions. Phys. Lett. A, 155: 269-275.
16. Liu S, Fu Z, Liu SD, Zhao Q (2001). Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A, 289: 69-74.
17. Lu D (2005). Jacobi elliptic function solutions for two variant Boussinesq equations. Chaos, Solitons Fract., 24: 1373-1385.
18. Miura MR (1978). Backlund Transformation, Springer-Verlag. Berlin.
19. Neirameh A, Ghasemi R, Roozi A (2010). Travelling wave solution for non-linear Klein- Gordon equation. Int. J. Phys. Sci., 5(16): 2528-2531.
20. Rogers C, Shadwick WF (1982). Backlund Transformations. Academic Press. New York.
21. Taghizade N, Neirameh A (2010). The solutions of TRLW and Gardner equations by (G′ / G) -expansion method. Int. J. Nonlinear Sci., 9(3): 305-310.
22. Wang Z, Zhang HQ (2007). Many new kinds exact solutions to (2+1)- dimensional Burgers equation and Klein-Gordon equation used a new method with symbolic computation. Appl. Math. Comput., 186: 693-704.
23. Wang M, Li X, Zhang J (2008). The (G′ / G) -expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A, 372: 417-423.
24. Wazwaz AM (2006). Analytical study of the fifth order integrable nonlinear evolution equations by using tanh method. Appl. Math Comput., 174: 289-299.
25. Wazwaz AM (2008a). New solutions of distinct physical structures to high-dimensional nonlinear evolution equations. Appl. Math. Comput., 196: 363-368.
26. Wazwaz AM (2008b). Multiple-soliton solutions for the fifth order Caudrey-Dood-Gibbon (CDG) equation. Appl. Math. Comput., 197: 719-724.
27. Weiss J, Tabor M, Garnevalle G (1983). The Painleve property for partial differential equations. J. Math. Phys., 24: 522-526.
28. Xu G (2006). An elliptic equation method and its applications in nonlinear evolution equations. Chaos, Solitons Fractals, 29: 942-947.
29. Yusufoglu E, Bekir A (2008). Exact solution of coupled nonlinear evolution equations. Chaos, Solitons and Fract., 37: 842-848.
30. Zayed EME, Zedan HA, Gepreel KA (2004). Group analysis and modified tanh-function to find the invariant solutions and soliton solution for nonlinear Euler equations. Int. J. nonlinear. Sci. Nume. Simul., 5: 221-234.
31. Zayed EME (2009a). The (G′ / G) -expansion method and its applications to some nonlinear evolution equations in the mathematical physics. J. Appl. Math. Comput., 30: 89-103.
32. Zayed EME (2009b). New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized (G′ / G) -expansion method. J. Phys. A: Math. Theor., 42: 195202-195214.
33. Zayed EME, Gepreel KA (2009). The (G′ / G) -expansion method for finding traveling wave solutions of nonlinear PDEs in mathematical physics. J. Math. Phys., 50: 013502-013513.
34. Zayed EME (2011). The (G′ / G) -expansion method combined with the Riccati equation for finding exact solutions of nonlinear PDEs. J. Appl. Math. Inform., 29(1-2): 351-367.
35. Zhang SL, Wu B, Lou SY (2002). Painleve analysis and special solutions of generalized Broer-Kaup equations. Phys. Lett. A, 300: 40-48.
36. Zhang S, Xia TC (2008). A further improved tanh-function method exactly solving the (2+1)-dimensional dispersive long wave equations. Appl. Math. E-Notes, 8: 58-66.
37. Zhang J, Wei X, Lu Y (2008). A generalized (G′ / G) -expansion method and its applications. Phys. Lett. A, 372: 3653-3658.
38. Zhang J, Jiang F, Zhao X (2010). An improved (G′ / G) -expansion method for solving nonlinear evolution equations. Int. J. Com. Math., 87(8): 1716-1725.