A computational approach to soliton solutions of the Kadomtsev±Petviashvili equation Abdul-Majid Wazwaz Department of Mathematics and Computer Science, Saint Xavier University, Chicago, IL 60655, USA Abstract In this paper, we present a computational approach to develop soliton solutions of the nonlinear Kadomtsev±Petviashvili equation. Our approach rests mainly on the Adomian decomposition method to include few components of the decomposition se- ries. The proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type. Numerical examples are tested to illustrate the proposed scheme. Ó 2001 Elsevier Science Inc. All rights reserved. Keywords: Kadomtsev±Petviashvili equation; Nonlinear evolution equation; Soliton; Adomian decomposition method 1. Introduction One of the most useful problems in nonlinear evolution was distinctively formulated by Kortweg and de Vries de®ned in the form u t 6luu x u xxx 0; l 1: 1 The Kortweg and de Vries KdV) equation 1) initiated an explanation of the phenomenon of solitary waves in weakly dispersing media. The KdV equation represents the longtime evolution of wave phenomena [1] in which Applied Mathematics and Computation 123 2001) 205±217 www.elsevier.com/locate/amc E-mail address: wazwaz@sxu.edu A.-M. Wazwaz). 0096-3003/01/$ - see front matter Ó 2001 Elsevier Science Inc. All rights reserved. PII:S0096-300300)00065-5