An Analysis of Modified Emden-Type Equation ẍ + αxẋ + βx3 = 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β - Natural Science

NS > Vol.11 No.1, January 2019

An Analysis of Modified Emden-Type Equation ẍ + αxẋ + βx³ = 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β ()

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DOI: 10.4236/ns.2019.111002 811 Downloads 1,472 Views Citations

Author(s)

D. Biswas

Affiliation(s)

Department of Physics (Formerly), Kalyani Mahavidyalaya, Kalyani, India.

ABSTRACT

The modified Emden-type is being investigated by mathematicians as well as physicists for about a century. However, there exist no exact explicit solution of this equation, ẍ + αxẋ + βx³ = 0 for arbitrary values of α and β. In this work, the exact analytical explicit solution of modified Emden-type (MEE) equation is derived for arbitrary values of α and β. The Lagrangian and Hamiltonian of MEE are also worked out. The solution is also utilized to find exact explicit analytical solution of Force-free Duffing oscillator-type equation. And exact explicit analytical solution of two-dimensional Lotka-Volterra System is also worked out.

KEYWORDS

Exact Analytical Solution, Lagrangian, Hamiltonian

Share and Cite:

Biswas, D. (2019) An Analysis of Modified Emden-Type Equation ẍ + αxẋ + βx³ = 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β. Natural Science, 11, 8-16. doi: 10.4236/ns.2019.111002.

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