Lie symmetries, Lagrangians and Hamiltonian framework of a class of nonlinear nonautonomous equations

Partha Guha and A. Ghose-Choudhury

Chaos, Solitons & Fractals, 2015, vol. 75, issue C, 204-211

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¨+53tq̇-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.

Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:75:y:2015:i:c:p:204-211

DOI: 10.1016/j.chaos.2015.02.021

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