Generalized solitary and periodic wave solutions to a (2 + 1)-dimensional Zakharov-Kuznetsov equation

Applied Mathematics and Computation

Volumn 217, Issue 4, 2010, Pages 1421-1429

  Aslan, Ismail ^a  

^a IZMIR INSTITUTE OF TECHNOLOGY   (Turkey)

Author keywords

Exp function method; Solitary wave solutions; Zakharov Kuznetsov equation

Indexed keywords

ATMOSPHERIC BLOCKING; COHERENT STRUCTURE; DIMENSIONAL MODEL; EXP-FUNCTION METHOD; EXPONENTIAL FUNCTION SOLUTION; PERIODIC WAVE SOLUTIONS; ROSSBY WAVE; SOLITARY WAVE SOLUTION; ZAKHAROV-KUZNETSOV EQUATION;

EXPONENTIAL FUNCTIONS; OCEAN CURRENTS; SOLITONS;

NONLINEAR EQUATIONS;

EID: 77957252477     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.05.037     Document Type: Article

References (53)

1. M.J. Ablowitz, and H. Segur Solitons and Inverse Scattering Transform 1981 SIAM Philadelphia
2. G.T. Liu, and T.Y. Fan New applications of developed Jacobi elliptic function expansion methods Phys. Lett. A 345 2005 161 166 (Pubitemid 41277056)
3. W. Malfliet, and W. Hereman The tanh method I: Exact solutions of nonlinear evolution and wave equations Phys. Scr. 54 1996 563 568 (Pubitemid 126631599)
4. A.M. Wazwaz Distinct variants of the KdV equation with compact and noncompact structures Appl. Math. Comput. 150 2004 365 377
5. G.W. Bluman, and S. Kumei Symmetries and Differential Equations 1989 Springer-Verlag New York
6. M.A. Abdou The extended F-expansion method and its application for a class of nonlinear evolution equations Chaos Solitons Fract. 31 2007 95 104 (Pubitemid 44038543)
7. R. Hirota The Direct Method in Soliton Theory 2004 Cambridge University Press Cambridge
8. J. Weiss, M. Tabor, and G. Carnevale The Painleve property for partial differential equations J. Math. Phys. 24 1983 522 526
9. M.L. Wang Exact solutions for a compound KdV-Burgers equation Phys. Lett. A 213 1996 279 287 (Pubitemid 126368639)
10. R.M. Miura Backlund Transformation 1996 Springer-Verlag New York
11. G. Adomian Solving Frontier Problems of Physics: The Decomposition Method 1994 Kluwer Boston
12. J.H. He A new approach to nonlinear partial differential equations Commun. Nonlinear Sci. Numer. Simul. 2 1997 230 235 (Pubitemid 40492053)
13. S.J. Liao Homotopy analysis method-A kind of nonlinear analytical technique not depending on small parameters Shanghai J. Mech. 18 1997 196 200
14. J.H. He An approximate solution technique depending on an artificial parameter: a special example Commun. Nonlinear Sci. Numer. Simul. 3 1998 92 97 (Pubitemid 40492026)
15. M. Wang, X. Li, and J. Zhang The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics Phys. Lett. A 372 2008 417 423 (Pubitemid 351329379)
16. . Aslan, and T. Özi Analytic study on two nonlinear evolution equations by using the (G′/G)-expansion method Appl. Math. Comput. 209 2009 425 429
17. . Aslan, and T. Özi On the validity and reliability of the (G′/G)-expansion method by using higher-order nonlinear equations Appl. Math. Comput. 211 2009 531 536
18. T. Özi, and. Aslan Symbolic computation and construction of new exact traveling wave solutions to Fitzhugh-Nagumo and Klein-Gordon equations Z. Naturforsch. 64a 2009 15 20
19. T. Özi, and. Aslan Symbolic computations and exact and explicit solutions of some nonlinear evolution equations in mathematical physics Commun. Theor. Phys. 51 2009 577 580
20. J.H. He, and X.H. Wu Exp-function method for nonlinear wave equations Chaos Solitons Fract. 30 2006 700 708 (Pubitemid 43903182)
21. J.H. He, and L.N. Zhang Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method Phys. Lett. A 372 2008 1044 1047
22. X.H. Wu, and J.H. He Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method Comput. Math. Appl. 54 2007 966 986 (Pubitemid 47488812)
23. J.H. He, and M.A. Abdou New periodic solutions for nonlinear evolution equations using Exp-function method Chaos Solitons Fract. 34 2007 1421 1429 (Pubitemid 46907583)
24. T. Özi, and. Aslan Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method Phys. Lett. A 372 2008 7011 7015
25. V.E. Zakharov, and E.A. Kuznetsov On three-dimensional solitons Soviet Phys. 39 1974 285 288
26. B.K. Shivamoggi The Painlevé analysis of the Zakharov-Kuznetsov equation Phys. Scr. 42 1990 641 642
27. S. Munro, and E.J. Parkes The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions J. Plasma Phys. 62 1999 305 317 (Pubitemid 129577916)
28. J. Das, A. Bandyopadhyay, and K.P. Das Stability of an alternative solitary-wave solution of an ion-acoustic wave obtained from the MKdV-KdV-ZK equation in magnetized non-thermal plasma consisting of warm adiabatic ions J. Plasma Phys. 72 2006 587 604 (Pubitemid 44024276)
29. A. Biswas, and E. Zerrad 1-soliton solution of the Zakharov-Kuznetsov equation with dual-power law nonlinearity Commun. Nonlinear Sci. Numer. Simul. 14 2009 3574 3577
30. H. Iwasaki, S. Toh, and T. Kawahara Cylindrical quasi-solitons of the Zakharov-Kuznetsov equation Physica D 43 1990 293 303
31. G.A. Gottwalld, The Zakharov-Kuznetsov equation as a two-dimensional model for nonlinear Rossby wave, arXiv: nlin, 0312009, 2003.
32. J.H. He Application of homotopy perturbation method to nonlinear wave equations Chaos Soliton Fract. 26 2005 695 700 (Pubitemid 40682499)
33. Z. Fu, S. Liu, and S. Liu Multiple structures of 2-D nonlinear Rossby wave Chaos Soliton Fract. 24 2005 383 390
34. X.W. Zhou, Y.X. Wen, and J.H. He Exp-function method to solve the nonlinear dispersive K(m, n) equations Int. J. Nonlinear Sci. Numer. Simul. 3 2008 301 306
35. X.H. Wu, and J.H. He EXP-function method and its application to nonlinear equations Chaos Soliton Fract. 38 2008 903 910 (Pubitemid 351633038)
36. M.A. Abdou, and E.M. Abulwafa Application of the Exp-function method to the Riccati equation and new exact solutions with three arbitrary functions of quantum Zakharov equations Z. Naturforsch. 63a 2008 646 652
37. V. Marinakis The Exp-function method find n-soliton solutions Z. Naturforsch. 63a 2008 653 656
38. C.Q. Dai, and Y.Y. Wang Exact travelling wave solutions of Toda lattice equations obtained via the Exp-function method Z. Naturforsch. 63a 2008 657 662
39. S. Zhang, W. Wang, and J.L. Tong The Exp-function method for the Riccati equation and exact solutions of dispersive long wave equations Z. Naturforsch. 63a 2008 663 670
40. S. Liu, Z. Fu, S. Liu, and Q. Zhao Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations Phys. Lett. A 289 2001 69 74 (Pubitemid 32964185)
41. A. Ebaid Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method Phys. Lett. A 365 2007 213 219
42. S.A. El-Wakil, M.A. Madkour, and M.A. Abdou Application of Exp-function method for nonlinear evolution equations with variable coefficients Phys. Lett. A 369 2007 62 69
43. S. Zhang Application of Exp-function method to a KdV equation with variable coefficients Phys. Lett. A 365 2007 448 453 (Pubitemid 351304390)
44. S. Zhang Exp-function method exactly solving a KdV equation with forcing term Appl. Math. Comput. 197 2008 128 134 (Pubitemid 351215484)
45. S. Zhang Exp-function method for constructing explicit and exact solutions of a lattice equation Appl. Math. Comput. 199 2008 242 249 (Pubitemid 351508328)
46. S.D. Zhu Discrete (2 + 1)-dimensional Toda lattice equation via Exp-function method Phys. Lett. A 372 2008 654 657
47. C. Dai, X. Cen, and S. Wu Exact travelling wave solutions of the discrete sine-Gordon equation obtained via the exp-function method Nonlinear Anal. 70 2009 58 63
48. C. Dai, X. Cen, S. Wu, The application of He's exp-function method to a nonlinear differential-difference equation, Chaos Solitons Fract., doi:10.1016/j.chaos.2008.02.021.
49. S. Zhang Application of Exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer-Kaup-Kupershmidt equations Phys. Lett. A 372 2008 1873 1880
50. C. Dai New exact solutions of the (3 + 1)-dimensional Burgers system Phys. Lett. A 373 2009 181 187
51. C. Dai, Y. Wang, New variable separation solutions of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, Nonlinear Anal., doi:10.1016/j.na.2008.12.052.
52. C. Dai, and J. Chen Exact solutions of (2 + 1)-dimensional stochastic Broer-Kaup equation Phys. Lett. A 373 2009 1218 1225
53. J. Zhu, New explicit exact solutions of the mKdV equation using the variational iteration method combined with Exp-function method, Chaos Solitons Fract., doi:10.1016/j.chaos.2007.08.051.