Symmetry Analysis and Conservation Laws of the Zoomeron Equation

Abstract

Abstract:In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the first time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the first time, we construct the conservation laws of the underlying equation using the multiplier method.

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

“…It provides the most effective and powerful techniques for obtaining closed-form solutions to NPDEs. For example, see [26][27][28][29][30][31][32][33]. It is worth noting here that the notion of a Galois group had influenced Lie's work on differential equations (DEs).…”

Symmetry Analysis and Conservation Laws of a Generalization of the Kelvin-Voigt Viscoelasticity Equation

“…This method called the multiplier method allows finding all local conservation laws admitted by any evolution equation. Many papers have been published in the last few years using this method [11][12][13][14][15][16][17][18][19].…”

Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

“…Several methods have been developed to find exact solutions of the NLPDEs. Some of these are the homogeneous balance method [12], the ansatz method [13], the inverse scattering transform method [14], the Bäcklund transformation [15], the Darboux transformation [16], the Hirota bilinear method [17], the simplest equation method [18], the (G /G)−expansion method [19,20], the Jacobi elliptic function expansion method [21], the Kudryashov method [22], the Lie symmetry method [23][24][25][26][27][28].…”

“…In Section 2 we determine the travelling wave solutions for the system (2a) using the Lie symmetry method along with the (G /G)−expansion method. Conservation laws for (2a) are constructed in Section 3 by employing the multiplier approach [26,[29][30][31][32][33][34][35][36][37]. Finally concluding remarks are presented in Section 4.…”