Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2009.3587.3592MirgolbabaeiH. GanjiD.D. 122009919In this study, He’s homotopy perturbation method is implemented for finding for solitary-wave solutions of the combined Korteweg de Vries-Modified Korteweg de Vries (KdV-MKdV) equation. Numerical solutions for the initial conditions has been obtained. The Homotopy Perturbation Method (HPM) deforms a difficult problem into a simple problem which can be easily solved. The results are compared with the exact solitary-wave solutions. The obtained solutions are compared with the Adomian’s decomposition method. All the examples show that the results of the present method are in excellent agreement with those obtained by the Adomian’s decomposition method.]]>Biazar, J., E. Babolian and R. Islam,2004147713719He, J.H.,2004151287292Fan, E.,200316819839Mohamad, M.N.B.,1992157378Yu, J.,20002316671670Hong, W.P.,2000115117118He, J.H.,19981675768He, J.H.,20003513743He, J.H.,2005347228230He, J.H.,200526695700He, J.H.,20063508788He, J.H.,20062011411199He, J.H.,20062025612568Ganji, D.D. and A. Rajabi,200633391400Rafei, M., D.D. Ganji, H. Danialia and H. Pashaei,2007305614620Ganji, D.D. and A. Sadighi,20067411418Hayat, T., M. Khan and S. Asghar,2004168213232Siddiqui, A.M., R. Mahmood and Q.K. Ghori,20067714Aabbasbandy, S.,2006175581589Zhang, L.N. and J.H. He,2006200616Abbasbandy, S.,2006172485490Koçak, H. and A. Yıldırım,200937331453150Berberler, M.E. and A. Yıldırım,20092009Al-Hayani, W. and L. Casasús,2005406778He, J.H.,199934699708He, J.H.,2000114115123Abdou, M.A. and A.A. Soliman, 2005181245251Wazwaz, A.M.,20062071823Sweilam, N.H. and M.M. Khader,200732145149Ganji, D.D., H. Mirgolbabaei, M. Miansari and M. Miansari,2008812561261Mirgolbabaei, H., D.D. Ganji and H. Taherian,200953844Mirgolbabaei, H., D.D. Ganji, M.M. Etghani and A. Sobati,20092009Omidvar, M., A. Barari, H. Mirgolbabaei and D.D. Ganji,20092009He, J.H.,1999178257262Ganji, D.D.,2006355337341