Based on the Homotopy Analysis Method to Solve the Klein - Gordon Equation


Article Preview

This paper applies the homotopy analysis method to solve Klein-Gordon equation, Firstly, structure a zero-order deformation equation. Then get the formal approximation of the model from high-order deformation equation and prove the effectiveness of the solution in the end.



Edited by:

Yun-Hae Kim and Prasad Yarlagadda




H. Y. Li et al., "Based on the Homotopy Analysis Method to Solve the Klein - Gordon Equation", Applied Mechanics and Materials, Vols. 278-280, pp. 62-67, 2013

Online since:

January 2013




[1] Liao Shi jun. Beyond the perturbation-Homotopy analysis Method Introduction[M]. Beijing: Science press. 2006. 11-44.

[2] Wu Qin kuan. Using the homotopy analysis method to solve a kind of combustion model[J]. Journal of Henan university of science and technology. 2010: 31(5)31-34.

[3] J.L. Zhang M.L. Wang X.Z. Li. The subsidiary ordinary differential equations And the exact solutions of the higher order dispersive nonlinear Schrödinger equation. Phys LettA, 2006, 357: 188-195.


[4] Dai Zhengde, Chen Shubao. Klein-Gordon equation new exact solution[R]. Yunnan university graduate student degree thesis. (2010).

[5] G.L. Xun, J.T. Pan. A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation. Communication of Theory Physies, 2008, 50: 1276-1278.


[6] Yang Lei, Zhou Zheng guang, Wang Ying hai. Exact solutions of nonlinear equations[ J]. Phys Lett, 1999, 260: 5-59.

[7] Liao Shi jun. Beyond the perturbatio: Homotopy analysis method basic thought and its application. Mechanics progress. (2008).

[8] Abbas Saadatmandi, Mehdi Dehghanb, Ali Eftekhari. Application of He's homotopy perturbation method for non-linear system of second-order boundary value problems. Nonlinear Analysis: Real World Applications, 2009, 10: 1912–(1922).


[9] J.H. He, Homotopy perturbation method: a new nonlinear technique [J]. Appl. Math. Compute. 2003, 135: 73-79.

[10] Liu su rong, Zhang zhong de, A Comparative Study Between the Variational Iteration Method and Adomian Decomposition Method-Based on the Study of Klein-Gordon equation. 2008: 5(4) 28-30.