Quantum mechanics

Pure mathematics

Bifurcation

Similarity (geometry)

Conjugacy class

Computer science

Classical mechanics

Physics

Nonlinear system

Mathematics

Image (mathematics)

Homogeneous space

Conservation law

Mathematical analysis

Artificial intelligence

Geometry

Traveling wave

Bifurcation theory

Mechanics

Pramana

The paper investigates a class of long-wave unstable lubrication model using Lie theory. A nonlinear self-adjoint classification of the considered equation is carried out. Without having to go into microscopic details of the physical aspects, non-trivial conservation laws are computed. Then, minimal set of Lie point symmetries of the discussed model is classified up to one-dimensional conjugacy classes which are further utilised one by one to construct the similarity variables to reduce the dimension of the considered model. After that, all possible phase trajectories are classified with respect to the parameters of the equation. Some travelling wave and kink-wave solutions are also showed and graphical representations are displayed to depict their propagation.

Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model