The modified (G'/G)-expansion method and traveling wave solutions of nonlinear the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 11, 2011, Pages 4259-4267

  Miao, Xiu Jin ^a   Zhang, Zai Yun ^a,b  

^a CENTRAL SOUTH UNIVERSITY   (China)

^b HUNAN FIRST NORMAL UNIVERSITY   (China)

Author keywords

NLSE with Kerr law nonlinearity; The modified (G' G) expansion method; Traveling wave solutions

Indexed keywords

CONTROL NONLINEARITIES; NONLINEAR EQUATIONS; OPTICAL KERR EFFECT; RATIONAL FUNCTIONS;

EXPANSION METHODS; KERR LAW NONLINEARITY; NONLINEAR SCHRÖDINGE EQUATION WITH KERR LAW NONLINEARITY; THE MODIFIED (G'/G)-EXPANSION METHOD; TRAVELING WAVE SOLUTION; TRIGONOMETRIC FUNCTIONS;

HYPERBOLIC FUNCTIONS;

EID: 79957901315     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.03.032     Document Type: Article

References (35)

1. Zhang Z.Y. New exact traveling wave solutions for the nonlinear Klein-Gordon equation. Turk J Phys 2008, 32:35-240.
2. Ma W.X., Fuchssteiner B. Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation. Int J Non-Linear Mech 1996, 31:29-338.
3. Zhang Z.Y., Liu Z.H., Miao X.J., Chen Y.Z. New exact solutions to the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. Appl Math Comput 2010, 216:64-3072.
4. Zhang Z.Y., Li Y.X., Liu Z.H., Miao X.J. New exact solutions to the perturbed nonlinear Schrodinger's equation with Kerr law nonlinearity via modified trigonometric function series method. Commun Nonlinear Sci Numer Simulat 2011, 16(8):97-3106.
5. Zhang Z.Y., Liu Z.H., Miao X.J., Chen Y.Z. Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. Phys Lett A 2011, 375(10):275-1280.
6. Yi{dotless}ldi{dotless}ri{dotless}m A., Pi{dotless}nar Z. Application of exp-function method for nonlinear reaction-diffusion equations arising in mathematical biology. Comput Math Appl 2010, 60(7):873-1880.
7. Ma W.X., Huang T.W., Zhang Y. A multiple exp-function method for nonlinear differential equations and its application. Phys Scr 2010, 82:065003.
8. Ma W.X., Lee J.-H. A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation. Choas Solitons Fractals 2009, 42:1356-1363.
9. Ma W.X., Chen M. Direct search for exact solutions to the nonlinear Schrödinger equation. Appl Math Comput 2009, 215:2835-2842.
10. Ma W.X., You Y. Solving the Korteweg-de Vries equation by its bilinear form: wronskian solutions. Trans Am Math Soc 2005, 357:1753-1778.
11. Wang M.L., Li X.Z., Zhang J.L. The G'G-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys Lett A 2008, 372:417-423.
12. Wang M.L., Zhang J.L., Li X.Z. Application of the G'G-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations. Appl Math Comput 2008, 206:321-326.
13. Bekir A. Application of the G'G-expansion method for nonlinear evolution equations. Phys Lett A 2008, 372:3400-3406.
14. Zhang S., Tong J.L. A generalized G'G-expansion method for the mKdV equation with variable coefficients. Phys Lett A 2008, 372:2254-2257.
15. Zhang S., Wang W., Tong J.L. A generalized G'G-expansion method and its application to the (2 + 1)-dimensional Broer-Kaup equations. Appl Math Comput 2009, 209:399-404.
16. Zayed E.M.E. The G'G-expansion method and its applications to some nonlinear evolution equations in the mathematical physics. J Appl Math Comput 2009, 30:89-103.
17. Aslan Ismail, Özis T. Analytic study on two nonlinear evolution equations by using the G'G-expansion method. Appl Math Comput 2009, 209:425-429.
18. Aslan Ismail, Özis T. On the validity and reliability of the G'G-expansion method by using higher-order nonlinear equations. Appl Math Comput 2009, 211:531-536.
19. Li B.Q., Ma Y.L. G'G-expansion method and new exact solutions for (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov system. Acta Phys Sin 2009, 58:4373-4378.
20. Ma Y.L., Li B.Q., Sun J.Z. New application of G'G-expansion method to high-dimensional nonlinear physical equations. Acta Phys Sinica 2009, 58:7402-7409.
21. Ebadi G., Biswas A. Application of the G'G-expansion method for nonlinear diffusion equations with nonlinear source. J Franklin Inst 2010, 347:1391-1398.
22. Biswas A. Theory of non-Kerr law solitons. Appl Math Comput 2004, 153(2):369-385.
23. Biswas A., Konar S. Introduction to non-Kerr Law optical solitons 2007, CRC Press, Boca Raton, FL, USA.
24. Biswas A. Perturbation of solitons with non-Kerr law nonlinearity. Choas, Solitons Fractals 2002, 13(4):815-823.
25. Biswas A., Milovic D. Bright and dark solitons of the generalized nonlinear Schrödinger's equation. Commun Nonlinear Sci Numer Simulat 2010, 15(6):1473-1484.
26. Biswas A., Porsezian K. Soliton perturbation theory for the modified nonlinear Schrödinger's equation. Commun Nonlinear Sci Numer Simulat 2007, 12(6):886-903.
27. Kohl R., Biswas A. Optical soliton perturbation in a non-Kerr law media. Optics Laser Technol 2008, 40(4):647-662.
28. Biswas A. Quasi-stationary optical solitons with parabolic law nonlinearity. Optics Commun 2003, 216:427-437.
29. Zakharov V.E., Shabat A.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov Phys JETP 1972, 34:62-69.
30. Zakharov V.E., Shabat A.B. Interaction between solitons in a stable medium. Sov Phys JETP 1973, 37:823-828.
31. Zhang H.Q. New exact complex travelling wave solutions to nonlinear Schrödinger (NLS) equation. Commun Nonlinear Sci Numer Simulat 2009, 14:668-673.
32. Liu J., Duan M.Y., Mu G., Wang C.J. Abundant exact solutions for the higher order non-linear Schrödinger equation with cubic-quintic non-Kerr terms. Commun Nonlinear Sci Numer Simulat 2010, 15:3777-3781.
33. Guo B.L., Chen H.L. Homoclinic orbit in a six-dimensional model of a perturbed higher-order nonlinear Schrödinger equation. Commun Nonlinear Sci Numer Simulat 2004, 9:431-441.
34. Bian C.Q., Pang J., Jin L.H., Ying X.M. Solving two fifth order strong nonlinear evolution equations by using G'G-expansion method. Commun Nonlinear Sci Numer Simulat 2010, 15:2337-2343.
35. Ma W.X., Fan E.G. Linear superposition principle applying to Hirota bilinear equations. Comput Math Appl 2011, 61:950-959.