Research Article Approximate Solution of Two-Dimensional Nonlinear Wave Equation by Optimal Homotopy Asymptotic Method H. Ullah, 1 S. Islam, 1 L. C. C. Dennis, 2 T. N. Abdelhameed, 3,4 I. Khan, 3 and M. Fiza 1 1 Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan 2 Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, 31750 Perak, Malaysia 3 College of Engineering Majmaah University, Majmaah, Saudi Arabia 4 Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt Correspondence should be addressed to L. C. C. Dennis; dennis.ling@petronas.com.my Received 2 October 2014; Revised 17 December 2014; Accepted 18 December 2014 Academic Editor: Haranath Kar Copyright © 2015 H. Ullah et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM). Te residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. Te resultant analytic series solution of the two-dimensional nonlinear wave equation shows the efectiveness of the proposed method. Te comparison of results has been made with the existing results available in the literature. 1. Introduction Te wave equations play a vital role in diverse areas of engi- neering, physics, and scientifc applications. An enormous amount of research work is already available in the study of wave equations [1, 2]. Tis paper deals with the two- dimensional nonlinear wave equation of the form  2 (,)  2 −(,)  2 (,)  2 =1−  2 + 2 2 , 0≤,≤1. (1) Te diferential equations (DEs) can be solved analyti- cally by a number of perturbation techniques [3, 4]. Tese techniques are fairly simple in calculating the solutions, but their limitations are based on the assumption of small parameters. Terefore, the researchers are on the go for some new techniques to overcome these limitations. Te idea of homotopy was pooled with perturbation. Liao [5] proposed homotopy analysis method (HAM) in his Ph.D. dissertation and applied it to various nonlinear engi- neering problems [6–8]. Te homotopy perturbation method (HPM) was initially introduced by He [9–13]. HPM has been extensively used by several researchers successfully for physical models [14–16]. Some useful comparisons between HAM and HPM were done by Domairry and Liang [17, 18]. Recently Marinca and Heris ¸anu [19–21] introduced OHAM for the solution of nonlinear problems which made the perturbation methods independent of the assumption of small parameters, and Ullah et al. [22–26] have extended and applied OHAM successfully for numerous nonlinear phenomena. Te motive of this paper is to apply OHAM for the solution of two-dimensional nonlinear wave equations. In [19–21] OHAM has been proved to be useful for obtaining an approximate solution of nonlinear diferential equations. Here, we have proved that OHAM is more useful and reliable for the solution of two-dimensional nonlinear wave equations, hence, showing its validity and greater potential for the solution of transient physical phenomenon in science and engineering. Section 2 has the basic idea of OHAM formulated for the solution of partial diferential equations. In Section 3, the efectiveness of OHAM for two-dimensional nonlinear wave equation has been studied. Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 380104, 7 pages http://dx.doi.org/10.1155/2015/380104