Lie Symmetries and Exact Solutions of Some Nonlinear PDEs

SEMINARIO DE ECUACIONES DIFERENCIALES

Conferenciante: Cihangir Özemi (Istanbul Technical University, Türkiye)

Abstract: The analysis of differential equations using Lie symmetries is an efficient method that has been used extensively in the literature, especially for nonlinear equations where the systematic tools available for analytical solutions are limited. The study of symmetry groups of differential equations reveals the symmetries of the equations originating from the physical nature of the problem. Determining the symmetry groups and algebras that leave the equations invariant, finding group-invariant exact analytical solutions, and classifying families of equations according to their symmetry algebras are some of the approaches used in this field. In this talk I will present results on Lie symmetry algebras of several equations of mathematical physics, including multidimensional Benney-Roskes system, the Rosenau equation and a higher order Boussinesq equation. Besides the invariance algebras I will mention several exact solutions, some of which have physical importance, like line solitons and lump solutions.