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Exact travelling wave solutions for a generalized Zakharov-Kuznetsov equation. (English) Zbl 1037.35070
Summary: By means of a proper transformation and symbolic computation, we study the exact travelling wave solutions for a generalized Zakharov-Kuznetsov (GZK) equation by using the extended-tanh method and direct assumption method. As a result, rich exact travelling wave solutions, which contain new kink-shaped solitons, bell-shaped solitons, periodic solutions, combined formal solitons, rational solutions and singular solitons for GZK equation, are obtained.

35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions
35-04Machine computation, programs (partial differential equations)
68W30Symbolic computation and algebraic computation
Full Text: DOI
[1] Ablowitz, M. J.; Clarkson, P. A.: Soliton, nonlinear evolution equations and inverse scatting. (1991) · Zbl 0762.35001
[2] Gu, C. H.: Soliton theory and its application. (1990)
[3] Wang, M. L.; Zhou, Y. B.; Li, Z. B.: Phys. lett. A. 216, 67-75 (1996) · Zbl 1125.35401
[4] Fan, E.; Zhang, H. Q.: Phys. lett. A. 246, 403-406 (1998) · Zbl 1125.35308
[5] Fan, E.: Phys. lett. A. 277, 212 (2000)
[6] Fan, E.: Phys. lett. A. 282, 18-22 (2001) · Zbl 0984.37092
[7] Fan, E.; Zhang, J.; Hon, B. Y. C.: Phys. lett. A. 291, 376 (2001)
[8] Yan, Z. Y.; Zhang, H. Q.: Phys. lett. A. 285, 355-362 (2001)
[9] Yan, Z. Y.: Phys. lett. A. 292, 100-106 (2001)
[10] Senthilelan, M.: Appl. math. Comp.. 123, 381 (2001)
[11] Zhang, W. G.; Chang, Q. S.; Jiang, B. G.: Chaos, solit. Fract.. 13, 311 (2002)
[12] Berezin, Y. A.; Karpman, V. I.: Sov. phys. JETP. 24, 1049 (1967)
[13] Washimi, M.; Taniuti, T.: Phys. rev. Lett.. 17, 996 (1966)
[14] Benney, D. J.: J. math. Phys. (Stud. Appl. math.). 45, 52 (1966)
[15] Kadomtsev, B. B.; Petviashvill, V. I.: Sov. phys. Dokl.. 15, 539 (1970)
[16] Zakharov, V. E.; Kuznetsov, E. A.: Sov. phys. JETP. 39, 285 (1974)
[17] Pelinovsky, D. E.; Grimshaw, R. H. J.: Physica D. 98, 139 (1996)
[18] Sipcic, R.; Benney, D. J.: Stud. appl. Math.. 105, 385 (2000)
[19] Wu, W.: D.z.du algorithms and computation. Algorithms and computation, 1 (1994)