Abstract
In this paper, Lie symmetry analysis is presented for the (3 + 1)-dimensional BKP-Boussinesq equation, which seriously affects the dispersion relation and the phase shift. To start with, we derive the Lie point symmetry and construct the optimal system of one-dimensional subalgebras. Moreover, according to the optimal system, similarity reductions are investigated and we obtain exact solutions of reduced equations by means of the Tanh method. In the end, we establish conservation laws using Ibragimov’s approach.
Highlights
In the past few years, nonlinear evolution equations have been used to explore physical phenomena, such as marine engineering, plasma physics, fluid dynamics, etc
We construct the optimal system of Equation (2), from which some interesting exact solutions are obtained by using the classical Tanh method [20,21]
We construct the optimal system of one-dimensional subalgebras
Summary
In the past few years, nonlinear evolution equations have been used to explore physical phenomena, such as marine engineering, plasma physics, fluid dynamics, etc. A very powerful method among those listed above, plays a significant role in obtaining exact solutions of PDEs. The basic idea of this method is to keep the solution set of the partial differential equations invariant under infinitesimal transformation. We construct the optimal system of Equation (2), from which some interesting exact solutions are obtained by using the classical Tanh method [20,21]. Another important aspect is conservation laws of PDEs which have important influence on finding solutions of PDEs [22,23]. The last section is made up of some brief statements
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