Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation

Abstract

In this paper we study a nonlinear multi-dimensional partial differential equation, namely, a generalized second extended (3+1)-dimensional Jimbo-Miwa equation. We perform symmetry reductions of this equation until it reduces to a nonlinear fourth-order ordinary differential equation. The general solution of this ordinary differential equation is obtained in terms of the Weierstrass zeta function. Also travelling wave solutions are derived using the simplest equation method. Finally, the conservation laws of the underlying equation are computed by employing the conservation theorem due to Ibragimov, which include conservation of energy and conservation of momentum laws.

A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

“…where c is a non-zero real value, required derivative terms are substituted into Eq. (2). By this way, the following nonlinear ordinary differential equation is obtained,…”

“…Hence, there are various analytical methods in the literature used by researchers to obtain solutions for such equations. Some of these are the multipliers method [1],the simplest equation method [2], the (G /G)-expansion method [3][4][5][6], the Sine-Gordon expansion method [7][8][9][10][11],the extended trial equation method [12,13], the new function method [14,15]. In this study, we used the Modified Exponential Function Method (MEFM) to the (3+1) dimensional Boiti-Leon-Manna-Pempinelli equation (BLMP) which is used to describe incompressible liquid in fluid mechanics.…”

Approximate Conservation Laws of Nonvariational Differential Equations

“…The multiplier approach in particular, has played a crucial role in several contexts [27][28][29][30][31]. Moreover, some recent studies of exact multipliers and conservation laws can be found in [32][33][34][35][36] and references therein.…”

Symmetry analysis and exact solutions of extended Kadomtsev-Petviashvili equation in fluids

“…Computing solutions of nonlinear partial differential equations (NLPDEs) is of importance to solve and understand the physical meaning of a given problem. To obtain the exact solutions of NLPDEs, researchers have come up with several methods, such as Kudryshov method [1], double reduction method [2], simplest equation method [3][4][5], homotopy analysis transform method [6], direct method [7], etc. The Lie's theory [8,9], introduced by Sophus Lie (1842-1899), is used to construct a symmetry reduction, and it can also play a major role in finding the exact solutions of partial differential equations (PDEs).…”