New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation


POLAT G. G. , Özer T.

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, vol.12, no.4, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1115/1.4035408
  • Title of Journal : JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS

Abstract

This study deals with the determination of Lagrangians, first integrals, and integrating factors of the modified Emden equation by using Jacobi and Prelle-Singer methods based on the Lie symmetries and lambda-symmetries. It is shown that the Jacobi method enables us to obtain Jacobi last multipliers by means of the Lie symmetries of the equation. Additionally, via the Lie symmetries of modified Emden equation, we analyze some mathematical connections between lambda-symmetries and Prelle-Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.