Application of the homotopy analysis method to solving nonlinear evolution equations. (Chinese. English summary) Zbl 1202.65130

Shi, Yuren; Xu, Xinjian; Wu, Zhixi; Wang, Yinghai; Yang, Hongjuan; Duan, Wenshan; Lü, Kepu

Acta Phys. Sin. 55, No. 4, 1555-1560 (2006).

Summary: We obtain a class of approximate periodic solutions for the \((2+1)\)-dimensional modified Zakharov-Kuznetsov equation by using the homotopy analysis method (HAM). The solutions we obtained agree with the exact solutions. The results indicate that the HAM is still valid for solving a class of higher dimensional evolution equations. We also made some efforts to extend the HAM to find the analytic solutions for more nonlinear evolution equations in an easier way.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53	KdV equations (Korteweg-de Vries equations)

Keywords:

homotopy analysis method; modified Zakharov-Kuznetsov equation; periodic solution