A General type of Liénard Second Order Differential Equation: Classical and Quantum Mechanical Study

  • Pravanjan Mallick North Orissa University

Abstract

We generate a general model of Liénard type of second order differential equation and study its classical solution. We also generate Hamiltonian from the differential equation and study its stable eigenvalues.

References

Geng L, Cai Xu-Chu (2007) He's frequency formulation for nonlinear oscillators. Eur J Phys 28: 923

Harko T, Lobo FSN, Mak MK (2013) A Chiellini type integrability condition for the generalized first kind Abel differential equation. Uni J Appl Math 1(2):101-104 (References cited there in)

He JH (2008a) An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int J Mod Phys B 22 (21): 3487-3578

He JH (2008b) Comment on 'He's frequency formulation for nonlinear oscillators. Eur J Phys 29: L19

Monsia MD, Akande J, Adjaї DKK, Koudahoun LH, Kpomahou YJF (2016) A Class of Position-Dependent Mass Liénard Differential Equations Via a General Nonlocal Transformation. viXra:1608.0226v1; Exact Analytical Periodic Solutions with Sinusoidal Form to a Class of Position-Dependent Mass Liénard-Type Oscillator Equations. viXra:1608.0368v1

Rath B (2008) Bogoliubov's canonical transformation approach on a harmonic oscillator: exponential decaying mass. Phys Scr 78: 065012

Rath B (2011) Some Studies on: Ancient Chinese Formalism, He’s Frequency Formulation for Nonlinear Oscillators and “Optimal Zero Work” Method. Orissa J Phys 18(1): 109-116

Rath B, Mallick P, Samal PK (2014) Real Spectra of Isospectral Non-Hermitian Hamiltonians. The African Rev Phys 9:0027: 201-205;Rath B (2015) Iso-spectral Instability of Harmonic Oscillator: Breakdown of Unbroken Pseudo-Hermiticity and PT Symmetry Condition. The African Rev Phys 10:0051:427-434
Published
2017-12-18
How to Cite
MALLICK, Pravanjan. A General type of Liénard Second Order Differential Equation: Classical and Quantum Mechanical Study. Proceedings of the Indian National Science Academy, [S.l.], v. 83, n. 4, p. 935-940, dec. 2017. ISSN 2454-9983. Available at: <http://insajournal.in/insaojs/index.php/proceedings/article/view/386>. Date accessed: 21 feb. 2018. doi: https://doi.org/10.16943/ptinsa/2017/49228.

Keywords

Liénard differential equation, classical solution, Hamiltonian, eigenvalues, matrix diagonalization method.