Quantization of quadratic Liénard-type equations by preserving Noether symmetries
From MaRDI portal
Publication:465218
DOI10.1016/j.jmaa.2014.09.045zbMath1320.34057arXiv1406.0192OpenAlexW2963038029MaRDI QIDQ465218
Maria Clara Nucci, Giorgio Gubbiotti
Publication date: 31 October 2014
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1406.0192
Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)
Related Items
Factorization technique and isochronous condition for coupled quadratic and mixed Liénard-type nonlinear systems, On connections of the Liénard equation with some equations of Painlevé-Gambier type, Ubiquitous symmetries, Quantization of the dynamics of a particle on a double cone by preserving Noether symmetries, The nonlinear pendulum always oscillates, Jacobi multipliers, non-local symmetries, and nonlinear oscillators
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quantum correction and ordering parameter for systems connected by a general point canonical transformation
- Equivalence classes of second-order ordinary differential equations with only a three-dimensional Lie algebra of point symmetries and linearisation.
- Lie symmetries, quantisation and \(c\)-isochronous nonlinear oscillators
- Exact quantization of a PT-symmetric (reversible) Liénard-type nonlinear oscillator
- General covariantxpmodels and the Riemann zeros
- Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier
- Lagrangians galore
- An algebraic approach to laying a ghost to rest
- Symmetries of differential equations. IV
- Symmetries of linear systems of second-order ordinary differential equations
- On the complete symmetry group of the classical Kepler system
- The solution of some quantum nonlinear oscillators with the common symmetry groupSL(2,R)
- Wavefunctions for the time-dependent linear oscillator and Lie point symmetries
- On a unique nonlinear oscillator
- Quantization of the Liénard II equation and Jacobi’s last multiplier
- Erratum: “Classification of Lie point symmetries for quadratic Liénard type equation $\ddot{x}+f(x)\dot{x}^2+g(x)=0$ẍ+f(x)ẋ2+g(x)=0” [J. Math. Phys. 54, 053506 (2013)]
- Quantizing preserving Noether symmetries
- Noether symmetries and the quantization of a Liénard-type nonlinear oscillator
- Jacobi Last Multiplier and Lie Symmetries: A Novel Application of an Old Relationship
- A class of solvable potentials
- A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator
- Jacobi’s last multiplier and Lagrangians for multidimensional systems
- Lie groups and quantum mechanics
