Lie symmetries, Lagrangians and Hamiltonian framework of a class of nonlinear nonautonomous equations Dedicated to the momory of Professor P.L. Sachdev.

Partha Guha, A. Ghose-Choudhury

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The method of Lie symmetries and the Jacobi Last Multiplier is used to study certain aspects of nonautonomous ordinary differential equations. Specifically we derive Lagrangians for a number of cases such as the Langmuir-Blodgett equation, the Langmuir-Bogulavski equation, the Lane-Emden-Fowler equation and the Thomas-Fermi equation by using the Jacobi Last Multiplier. By combining a knowledge of the last multiplier together with the Lie symmetries of the corresponding equations we explicitly construct first integrals for the Langmuir-Bogulavski equation q +53/tq-t-5/3q-1/2=0 and the Lane-Emden-Fowler equation. These first integrals together with their corresponding Hamiltonains are then used to study time-dependent integrable systems. The use of the Poincaré-Cartan form allows us to find the conjugate Noetherian invariants associated with the invariant manifold.

Original languageBritish English
Pages (from-to)204-211
Number of pages8
JournalChaos, Solitons and Fractals
Volume75
DOIs
StatePublished - Jun 2015

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