In this paper, variational iteration method (VIM) is applied to obtain approximate analytical solution of the (2 + 1)-dimensional potential Kadomtsev-Petviashvili equation (PKP) without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

In this work, a Lie group reduction for (2 + 1) dimensional fractional Kadomtsev-Petviashvili (KP) system is determined by using the symmetry method with Riemann Liouville derivative. After reducing into two-dimensional nonlinear partial differential (NLFPDEs), power series (PS) applied to obtain exact solution. Further obtained solution analyzed convergence. Then, new conservation theorem gene...

Of concern are traveling wave solutions for the fractional Kadomtsev–Petviashvili (fKP) equation. The existence of periodically modulated solitary is proved by dimension-breaking bifurcation. Moreover, line and their transverse (in)stability discussed. Analogous to classical Kadmomtsev–Petviashvili (KP) equation, fKP equation comes in two versions: fKP-I fKP-II. We show that waves transversely ...

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived. Keywords—Hirota bilinear method, potential KadomtsevPetviashvili equation, Multiple sol...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

This paper obtains the soliton solution for the Calogero–Degasperis and the potential Kadomtsev–Petviashvili equations. The tanh–coth and the tan–cot methods are used to retrieve the solutions. Finally, the ansatz method is also used to integrate these equations with any arbitrary constant coefficients. Finally, a fewnumerical simulations are also given. © 2011 Elsevier Ltd. All rights reserved.

The spectrum of a Schrödinger operator with a perfect honeycomb lattice potential has special points, called Dirac points where the lowest two branches of the spectrum touch. Deformations can result in the merging and disappearance of the Dirac points and the originally intersecting dispersion relation branches separate. Corresponding to these deformations, nonlinear envelope equations are deri...