Abstract
In this paper we analyse a (3+1)-dimensional generalized Kadomtsev-Petviashvili-Boussinesq equation, which describes the evolution of shallow water waves. This equation was formulated not long ago, by including the term uttto the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation. Invoking the Lie symmetry methods we perform several symmetry reductions and reduce the equation to a fourth-order nonlinear ordinary differential equation. Consequently, this ordinary differential equation is solved and its general solution is derived connected with Weierstrass zeta function. The profiles of solutions are displayed graphically. In addition to those, we construct some travelling waves by engaging Kudryashov’s method. To complete our study we finally derive some conservation laws of the equation under consideration by appealing to the Ibragimov’s conservation theorem.
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