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Explicit solutions of the Bogoyavlensky-Konoplechenko equation. (English) Zbl 1184.35285
Summary: By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the Bogoyavlensky-Konoplechenko equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the BK equation. Then we get the reductions using the symmetry and give some exact solutions of the BK equation.

35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form
35B06Symmetries, invariants, etc. (PDE)
Full Text: DOI
[1] Yan, Z. L.; Liu, X. Q.: Symmetry and similarity solutions of variable coefficients generalized Zakharov -- Kuznetsov equation, Appl. math. Comput. 180, 288-294 (2006) · Zbl 1109.35101 · doi:10.1016/j.amc.2005.12.021
[2] Dong, Z. Z.; Liu, X. Q.; Bai, C. L.: Symmetry reduction, exact solutions, and conservation laws of (2+1)-dimensional Burgers Korteweg -- de Vries equation, Commun. theor. Phys. (Beijing, China) 46, 15-20 (2006)
[3] Prabhakar, M. V.; Bhate, H.: Exact solutions of the Bogoyavlensky -- Konoplechenko equation, Lett. math. Phys. 64, 1-6 (2003) · Zbl 1021.37042 · doi:10.1023/A:1024909327151
[4] Hu, H. C.: New positon, negaton and complexiton solutions for the Bogoyavlensky -- Konoplechenko equation, Phys. lett. A 373, 1750-1753 (2009) · Zbl 1229.37070 · doi:10.1016/j.physleta.2009.03.022
[5] Calogero, F.: A method to generate solvable nonlinear evolution equations, Lett. nuovo cimento 14, 443-447 (1975)
[6] Bogoyavlenskii, O. I.: Overturning solitons in new two-dimensional integrable equations, Izv. akad. Nauk SSSR ser. Mat. 53, 243-257 (1989) · Zbl 0712.35083 · doi:10.1070/IM1990v034n02ABEH000628
[7] Toda, K.; Yu, S. J.: A study of the construction of equations in (2+1)-dimensions, Inverse problems 17, 1053-1060 (2001) · Zbl 0985.35088 · doi:10.1088/0266-5611/17/4/331
[8] Konopelchenko, B. G.: Solitons in multidimensions, (1993) · Zbl 0836.35002
[9] Wang, M. L.; Li, X. Z. .; Zhang, J. L.: The $G^{\prime}$G-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. lett. A 372, 417-423 (2008) · Zbl 1217.76023 · doi:10.1016/j.physleta.2007.07.051