On the application of the Exp-function method to the KP equation for N-soliton solutions

Abstract

a b s t r a c tWe observe that the form of the Kadomstev-Petviashvili equation studied by Yu (2011) [S. Yu, N-soliton solutions of the KP equation by Exp-function method, Appl. Math. Comput. (2011) doi:10.1016/j.amc.2010.095] is incorrect. We claim that the N-soliton solutions obtained by means of the basic Exp-function method and some of its known generalizations do not satisfy the equation considered. We emphasize that Yu's results (except only one) cannot be solutions of the correct form of the Kadomstev-Petviashvili equation. In addition, we provide some correct results using the same approach.Ó 2012 Elsevier Inc. All rights reserved.As is well known, the Kadomstev-Petviashvili equation ( where the coefficients a, b, and c can be chosen appropriately. In the literature, one can encounter some distinct forms of the KP equation such as KPI equation (the case a ¼ 6, b ¼ 1, c ¼ À3 of (1)) and KPII equation (the case a ¼ 6, b ¼ 1, c ¼ 3 of (1) (1) The author considers the KP equation asand claims that Eq. (2) admits the one-soliton solution (the formula (9) in [2]) uðx; y; tÞwhere b 1 , k 1 , and r 1 remain arbitrary. But, the formula (2) describes two equations which differ in the sign of their u yy -terms. The author does not mention which equation in (2) admits the function (3) as a solution. Moreover, the direct substitution of (3) into (2) results in the expression 0096-3003/$ -see front matter Ó

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