Lie Symmetries and Exact Solutions for a Nonlinear Evolution Equation in the AKNS Hierarchy

Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries

‎In this paper Lie symmetry analysis is applied to find new‎ solution for Fokker Plank equation of geometric Brownian motion‎. This analysis classifies the solution format of the Fokker Plank‎ ‎equation‎.

Lie symmetries and exact solutions of barotropic vorticity equation

The Lie group method is used in order to investigate various issues related to symmetries and exact solutions of the barotropic vorticity equation. This is done in a similar but more systematic and complete way as given by Huang and Lou [Phys. Lett. A. 320 (2004) 428–437]. The Lie symmetries of the barotropic vorticity equations on the f and β-planes as well as on the sphere in rotating and res...

Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

New Solutions for Fokker-Plank Equation of‎ ‎Special Stochastic Process via Lie Point Symmetries

‎In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of Ornstein-Uhlenbeck process‎. ‎This analysis classifies the solutions format of the Fokker Plank equation by using the Lie algebra of the symmetries of our considered stochastic process‎.

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow