Exact Solutions and Conservation Laws of a (2+1)-Dimensional Nonlinear KP-BBM Equation

Abstract

In this paper, we study the two-dimensional nonlinear Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation. This equation is the Benjamin-Bona-Mahony equation formulated in the KP sense. We first obtain exact solutions of this equation using the Lie group analysis and the simplest equation method. The solutions obtained are solitary waves. In addition, the conservation laws for the KP-BBM equation are constructed by using the multiplier method.

Conservation Laws of Two(2+1)-Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives

“…The correctness of the conservation laws of (2) obtained here has been checked by Maple software. The conservation laws obtained here for (2) are much more than those in [24] and different from them.…”

“…Abdou [23] used the extended mapping method with symbolic computation to obtain some periodic solutions, solitary wave solution, and triangular wave solution. Exact solutions and conservation laws of (2) have been studied by Adem and Khalique using the Lie group analysis and the simplest equation method [24].…”

Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

“…During the past few decades various integration techniques have been developed by the researchers to solve these NLEEs. Some of the well-known techniques used in the literature are the inverse scattering transform method [1], the homogeneous balance method [2], the Bäcklund transformation [3], the Weierstrass elliptic function expansion method [4], the Darboux transformation [5], the ansatz method [6,7], Hirota's bilinear method [8], the ( / )-expansion method [9], the Jacobi elliptic function expansion method [10,11], the variable separation approach [12], the sine-cosine method [13], the trifunction method [14,15], the F-expansion method [16], the exp-function method [17], the multiple exp-function method [18], and the Lie symmetry method [19][20][21][22][23][24][25].…”

Solutions and Conservation Laws of a (2+1)-Dimensional Boussinesq Equation

“…Nevertheless, in the last few decades important progress has been made and many powerful and effective methods for obtaining exact solutions of NLEEs have been suggested in the literature. Some of the important methods found in the literature include the Darboux transformation method [1], the inverse scattering transform method [2], Hirota's bilinear method [3], Jacobi elliptic function expansion method [4], the sine-cosine method [5], the auxiliary ordinary differential equation method [6], Lie symmetry analysis [7][8][9][10][11], the -expansion method [12], and the exp-function expansion method [13].…”