Physics

Burgers' equation

Nonlinear system

Pure mathematics

Symmetry (geometry)

Mathematics

Mathematical physics

Infinitesimal

Partial differential equation

Mathematical analysis

Kadomtsev–Petviashvili equation

Power (physics)

Geometry

Lie algebra

Quantum mechanics

Generator (circuit theory)

Differential equation

Conjugacy class

Conservation law

Ordinary differential equation

Results in Physics

In this paper, the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation is taken into consideration by means of Lie symmetry analysis. Infinitesimal generators are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Henceforth, conjugacy classes of abelian algebra are used to find the similarity reductions, which convert the considered equation into ordinary differential equations (ODEs). Further, these ODEs are taken into consideration, and travelling wave structures are computed by applying different techniques. Moreover, the discussed model is discussed by means of nonlinear selfadjointness and conservation laws are derived for each Lie symmetry generator. For specific values of the physical parameters of the equation under discussion, the graphical behaviour of some solutions is depicted.

Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation