Open Access
Subscription Access
Open Access
Subscription Access
Similarity Solutions of Non-Autonomous Lienard Type Equations
Subscribe/Renew Journal
In this paper, we obtain similarity solutions of non-autonomous Lienard type equation. First integrals of Lienard type equations are obtained by non-holonomic transformations and these rst integrals are integrated by Lie group analysis.
Keywords
Lienard Type Equation, Lie Group Symmetry, Non-Linear Oscillators, Non-Holonomic Transformation.
Subscription
Login to verify subscription
User
Font Size
Information
- Tomas Caraballo and David Cheban, Almost periodic and asymptotically almost periodic solutions of Lienard equation, Discrete and Continuous Dynamical Systems - Series B (DCDS-B), 16(3), (2011), 703-717.
- V. K. Chandrasekar, M. Senthilvelan and M. Lakshamanan, On Complete integrability and linearization of certain second order nonlinear ordinary differential equations, Proc. Royal Soc. A., 461, (2005), 2451 - 2477, doi:10.1098/rspa.2005.1465.
- V. K. Chandrasekar, S. N. Pandey , M. Senthilvelan and M. Lakshamanan, A simple and unified approach to identify integrable nonlinear oscillators and systems, J. Maths. Phys., 47(2), (2006), Sr. No.-023508.
- Parth Guha, A. Ghose Choudhary and Barun Khanra, First integrals for time dependent higher order Riccati equations by non-holonomic transformation, Commun. Nonlinear Sci. Numer Simulat, 16 (8), (2011), 3062-3070.
- Tiberiu Harko, Francisco S. N. Lobo and M. K. Mak, A class of exact solutions of the Lienard type ordinary non-linear differential equation, J. Engineering Maths., 89(1), (2014), 193-205.
- Tiberiu Harko and Shi Dong Liang, Exact solutions of the Lienard and generalized Lienard type ordinary non-linear differential equations obtained by deforming the phase space coordinates of the linear harmonic oscillator, To appear in J. Engineering Maths., arXiv:1505.02364v3 [math-ph], 28 Jauary 2015.
- L. Herrmann, Oscillations for Lienard type equations, J. Math. Pures Appl., 90(1), (2008), 60-65.
- H. Kleinert, Path integrals in quantum mechanics, statistics, polymer physics, and financial markets, World Scientic, 2009.
- H. Kleinert, Nonholonomic mapping principle for classical and quantum mechanics in spaces with curvature and torsion, General Relativity and Gravitation, 32 (5), (2000), 769-839.
- M. Lakshmanan and V. K. Chandrasekar, Generating Finite Dimensional Integrable Nonlinear Dynamical Systems, European Physical J. Special Topics, 222 (3-4), (2013), 665-688.
- P. J. Olver, Application of Lie Groups to Differential Equations, Graduate Texts in Mathematics, Springer-Verlag, New York, Volume-107, 1986.
- S. N. Pandey, P. S. Bindu, M. Senthilvelan and M. Lakshmanan , A group theoretical identification of integrable cases of the Lienard-type equation x + f(x)x + g(x) = 0.I. Equations having non-maximal number of Lie point symmetries, J. Math. physics, 50(8), (2009), Sr.No.-082702.
- S. N. Pandey, P. S. Bindu, M. Senthilvelan and M. Lakshmanan , A group theoretical identification of integrable cases of the Lienard-type equation x + f(x)x + g(x) = 0: II.Equations having maximal number of Lie point symmetries, J. Math. physics, 50(8), (2009), Sr.No.- 102701.
- S. H. Thakar, The general solution of generalized Emden-Fowler equation, Bull. Kerala Maths. Assoc., 9(2), (2012), 285-295.
Abstract Views: 233
PDF Views: 1