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

Abstract

Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid of ( / )-expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method.

Lie symmetries and conservation laws for a generalized Kuramoto‐Sivashinsky equation

“…Many recent papers using this method are in the literature. [25][26][27] The aim of this paper is to consider the following generalization of Equations 1 and 2:…”

Conservation laws for a strongly damped wave equation

“…In [2][3][4][5], Anco and Bluman gave a general algorithmic method to find all conservations laws for evolution equations Many recent papers using this method have been published in [1,11,12]. After Ibragimov's results several papers appeared concerned with self-adjointness and its applications to PDEs [22,23].…”

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

“…1. Introduction 38 Fractional partial differential equations (FPDEs) appear in vari- 39 ous research and engineering applications such as physics, biology, 40 rheology, viscoelasticity, control theory, signal processing, systems 41 identification and electrochemistry [1][2][3][4][5][6][7][8]. Recently, they have 42 attracted considerable interest and there has been a significant 43 theoretical development in this area.…”

“…In the last few decades, Lie's method has 59 been described in a number of excellent textbooks and has been 60 applied to a number of physical and engineering models. [35][36][37][38][39]. 88 The family of seventh-order Korteweg-de Vries (KdV) equations 89 are given by [40] x ¼ x þ nðx; t; uÞ þ Oð 2 Þ; and D x denotes the total differentiation operator defined by (9) is given by [16,17] It should be noted that we have l ¼ 0 when the infinitesimal g is 208 linear in u, because of the existence of the derivatives @ k g @u k ; k P 2 in 209 the above expression.…”

“…. .Þ ¼ 0; 0 < a 6 1: Step 3: Substituting (40) into (39) and setting the coefficients of 511 / i to be zero, one obtains an over-determined nonlinear algebraic 512 system in a i (i ¼ 1; . .…”