J Austral Math Soc Ser B 32 pp457--468, 1991.

On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance

O. P. Bhutani and K. Vijayakumar

Abstract

After formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.

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Authors

O. P. Bhutani

Department of Mathematics, Indidan Institute of Technology, Hauz Khas, New Delhi-110016.

K. Vijayakumar

Department of Mathematics, Panjab University, Chandigarh, India.