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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.

Exact Solutions and Conservation Laws of the (3 + 1)-Dimensional B-Type Kadomstev–Petviashvili (BKP)-Boussinesq Equation