Symmetry solutions and conservation laws of a (3+1)-dimensional generalized KP-Boussinesq equation in fluid mechanics. (English) Zbl 07848654
Summary: 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 \(u_{tt}\) to 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.
MSC:
| 35Qxx | Partial differential equations of mathematical physics and other areas of application |
| 35Cxx | Representations of solutions to partial differential equations |
| 37Kxx | Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
(3+1)-dimensional generalized KP-Boussinesq equation; Lie symmetries; solitons; analytic solutions; Weierstrass zeta function; conservation lawsReferences:
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