Seyed-Reza Hejazi | Searcharxiv

arXiv2008

Lie Symmetries and Solutions of KdV Equation

Symmetries of a differential equations is one of the most important concepts in theory of differential equations and physics. One of the most prominent equations is KdV (Kortwege-de Vries) equation with application in shallow water theory. In this paper we are going to explain a particular method for finding symmetries of KdV equation, which is called Harrison method. Our tools in this method are Lie derivatives and differential forms, which will be discussed in the first section more precisely. In second chapter we will have some analysis on the solutions of KdV equation and we give a method, which is called first integral method for finding the solutions of KdV equation.

math-ph↗

arXiv2008

Symmetries of 2nd order ODE: y'' + G(x)y' + H(x)y = 0

This paper is devoted to study the Lie algebra of linear symmetries of a homogenous 2nd order ODE, by the method of Kushner, Lychagin and Robstov.

math.DG↗

arXiv2008

Differential Invariants of SL(2) and SL(3)-ACTIONS on R^2

The main purpose of this paper is calculation of differential invariants which arise from prolonged actions of two Lie groups SL(2) and SL(3) on the $n$th jet space of $R^2$. It is necessary to calculate $n$th prolonged infenitesimal generators of the action.

math.DG↗