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 λ-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 λ-symmetries and Prelle–Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.
New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation
Department of Mathematics,
İstanbul Technical University,
Maslak, İstanbul 34469, Turkey
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 1, 2016; final manuscript received November 15, 2016; published online January 19, 2017. Assoc. Editor: Firdaus Udwadia.
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Gün Polat, G., and Özer, T. (January 19, 2017). "New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation." ASME. J. Comput. Nonlinear Dynam. July 2017; 12(4): 041001. https://doi.org/10.1115/1.4035408
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