An Analysis of Modified Emden-Type Equation ẍ+ αxẋ+ βx<sup>3</sup>= 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β

• 作者: D. Biswas
• 来源期刊: 自然科学期刊(英文)
• 学科: 数学
• 关键词: EXACT Analytical Solution LAGRANGIAN HAMILTONIAN
• 年，卷（期）: zrkxqkyw_2019,（1）
• 页码范围: 8-16
• 页数: 9页
• 分类号: O1

摘要

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.