The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-B...

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K-P equation (Kadomtsev & Petviashvili 1970) to incl...

In this paper, the sine-cosine, the standard tanh and the extended tanh methods has been used to obtain solutions of the KadomstevPetviashvili(KP) equation. New solitons solutions and periodic solutions are formally derived. The change of parameters, that will drastically change characteristics of the equation, is examined.

The dispersionless Kadomtsev-Petviashvili (dKP) equation (ut + uux)x = uyy is one of the simplest nonlinear wave equations describing twodimensional shocks. To solve the dKP equation we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation ut + uux = 0. We show numerically that the solutions to the transformed equation develops singulari...