Article ID Journal Published Year Pages File Type
8254949 Chaos, Solitons & Fractals 2015 8 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Physics and Astronomy Statistical and Nonlinear Physics
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