Abstract
Abstract Studies on Non-linear evolutionary equations have become more critical as time evolves. Such equations are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, the Lie group theory is used to apply the similarity reduction and to find some exact solutions of a (3+1) dimensional nonlinear evolution equation. In this report, the groups of symmetries, Tables for commutation, and adjoints with infinitesimal generators were established. The subalgebra and its optimal system is obtained with the aid of the adjoint Table. Moreover, the equation has been reduced into a new PDE having less number of independent variables and at last into an ODE, using subalgebras and their optimal system, which gives similarity solutions that can represent the dynamics of nonlinear waves.
Highlights
Non-linear governing equations suitable to analyze quartic autocatalysis were presented by Makinde and Animasaun in [1] and [2]
The equation has been reduced into a new PDE having less number of independent variables and at last into an ODE, using subalgebras and their optimal system, which gives similarity solutions that can represent the dynamics of nonlinear waves
We aim to extend the work in [8], where the classical Lie symmetry of the (3+1)-dimensional nonlinear evolution equation (1) was found
Summary
Non-linear governing equations suitable to analyze quartic autocatalysis were presented by Makinde and Animasaun in [1] and [2]. The (3+1) dimensional nonlinear evolution equations was rst introduced by Zhaqilao [3] in the study of algebraic-geometrical solutions. Xin Zhao et al [27] have investigated the generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics, uid mechanics and plasma physics They have used the Hirota Bilinear method, and obtained bilinear Bäcklund transformation, to construct the Lax pair and obtained Mixed Rogue– Solitary Wave Solutions, Rogue–Periodic Wave Solutions and Lump-Periodic Wave Solutions. Dimensional nonlinear evolution equation is obtained by using the Hirota bilinear method with the perturbation technique in [6]. A new Wronskian condition was set for equation (1), with the aid of the Hirota bilinear transformation, a novel Wronskian determinant solution is presented for the equation (1). In section (4), we investigated the reduced equations to nd exact solutions, and in the end, some remarks are presented in the conclusion
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