A class of solvable coupled nonlinear oscillators with amplitude independent frequencies

Chandrasekar, V. K.; Sheeba, Jane H.; Pradeep, Ronak; Divyasree, R.S.a b; Lakshmanan, M.

doi:10.1016/j.physleta.2012.04.058

Cited by 29 publications

(37 citation statements)

References 17 publications

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“…Since then Liénard equations have been applied to many different areas even in biology [19]. The particular Liénard equation (5) has been extensively studied by many authors, the most recent papers being [20][21][22][23]. In [24][25][26] Lie group analysis was applied to (6) and it was shown that equation (5) is the only linearizable equation among those in (6).…”

Section: Classical Properties Of the Liénard Equation (5)mentioning

confidence: 99%

Noether symmetries and the quantization of a Liénard-type nonlinear oscillator

Gubbiotti

Nucci

2021

JNMP

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The classical quantization of a Liénard-type nonlinear oscillator is achieved by a quantization scheme (M. C. Nucci. Theor. Math. Phys., 168:994-1001, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. This method straightforwardly yields the Schrödinger equation in the momentum space as given in (V. Chithiika Ruby, M. Senthilvelan, and M. Lakshmanan. J. Phys. A: Math. Gen., 45:382002, 2012), and sheds light on the apparently remarkable connection with the linear harmonic oscillator.

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Section: Classical Properties Of the Liénard Equation (5)mentioning

confidence: 99%

Noether symmetries and the quantization of a Liénard-type nonlinear oscillator

Gubbiotti

Nucci

2021

JNMP

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“…[8][9][10][11] The mathematical properties of LT equations in its general form have been intensively exercised, and their study remains an active field of research in applied sciences and engineering. [8][9][10][11][12][13][14][15][16][17][18][19][20][21] Recently, in a series of work, Harko and his collaborators studied various aspects of GL and LT equations in different forms. [8][9][10][11] In their works, they tried to establish the integrability conditions of a variety of GL/LT equations through their reduction to first-order equations of Riccati or Abel type.…”

Section: Introductionmentioning

confidence: 99%

Piecewise smooth localized solutions of Liénard‐type equations with application to NLSE

Das

Mandal

Panja

2018

Math Methods in App Sciences

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In this work, the rapidly convergent approximation method (RCAM) followed by appropriate modifications is applied to obtain piecewise smooth solutions and conserved quantities of a Liénard‐type equation and some important nonlinear partial differential equations reducible to former one. Explicit parameter dependence of the solution has been sensibly used to determine parameter dependence of the constant of the motion as well as the domain in the parameter space for which the piecewise smooth solution is bounded. Solution of Liénard‐type equation is then used to find piecewise smooth traveling wave solutions and corresponding conserved quantities of nonlinear Schrödinger equation. These findings affirm the efficiency of the RCAM for analytical exercise of variety of nonlinear systems of ordinary/partial differential equations appear as mathematical model of physical processes.

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“…In [24] the same quantization scheme was applied in order to quantize the second-order Riccati equation while in [25] the quantization of Calogero's goldfish system was achieved. In [11] it was shown that this method straightforwardly yields the Schrödinger equation in the momentum space of a Liénard-type nonlinear oscillator as given in [4].…”

Section: Introductionmentioning

confidence: 99%