Application of the homotopy perturbation method to Zakharov-Kuznetsov equations. (English) Zbl 1189.65244

Biazar, J.; Badpeima, F.; Azimi, F.

Comput. Math. Appl. 58, No. 11-12, 2391-2394 (2009).

Summary: The aim of this paper is to apply the homotopy perturbation method (HPM) to solve the Zakharov-Kuznetsov \(ZK(m,n,k)\) equations. The two special cases, \(ZK(2, 2, 2)\) and \(ZK(3, 3, 3)\), are chosen to show the ability of the method. General formulas for the solutions of \(ZK(m,n,k)\) are established. The results reveal that the method is very effective and simple.

MSC:

65M99

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

Keywords:

Zakharov-Kuznetsov equations; homotopy perturbation method

References:

[1]	He, J. H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg., 178, 257-262 (1999) · Zbl 0956.70017
[2]	He, J. H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Internat. J. Non-Linear Mech., 35, 37-43 (2000) · Zbl 1068.74618
[3]	He, J. H., the homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput., 156, 591-596 (2004) · Zbl 1061.65040
[5]	Monro, S.; Parkers, E. J., J. Plasma Phys., 62, 305 (1999)
[6]	Zakharov, V. E.; Kuznetsov, E. A., Sov. Phys., 39, 285 (1974)
[7]	Mustafa Inc, Exact solution with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion, Chaos Solitons Fractals, 33, 1783-1790 (2007) · Zbl 1129.35450