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

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  • Guha, Partha
  • Ghose-Choudhury, A.

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.

Suggested Citation

  • Guha, Partha & Ghose-Choudhury, A., 2015. "Lie symmetries, Lagrangians and Hamiltonian framework of a class of nonlinear nonautonomous equations," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 204-211.
    • Handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:204-211
    DOI: 10.1016/j.chaos.2015.02.021
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    Cited by:

    1. Bruzón, M.S. & Garrido, T.M. & de la Rosa, R., 2016. "Conservation laws and exact solutions of a Generalized Benjamin–Bona–Mahony–Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 578-583.
    2. Zhang, Yi, 2019. "Lie symmetry and invariants for a generalized Birkhoffian system on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 306-312.

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