On the linearization of isochronous centre of a modified Emden equation with linear external forcing

Mohanasubha, R.; Shakila, M.I. Sabiya; Senthilvelan, M.

doi:10.1016/j.cnsns.2013.08.005

Cited by 6 publications

(3 citation statements)

References 27 publications

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“…where we have chosen k 2 = 0. The above equation is well known in the literature and has been studied by many authors in different perspectives [4,5,12,14,31]. Using the results given in Sec.…”

Section: F (X) =mentioning

confidence: 99%

The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective

et al. 2016

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In this paper, we discuss the inverse problem for a mixed Liénard type nonlinear oscillator equationẍ + f (x)ẋ 2 + g(x)ẋ + h(x) = 0, where f (x), g(x) and h(x) are arbitrary functions of x. Very recently, we have reported the Lie point symmetries of this equation. By exploiting the interconnection between Jacobi last multiplier, Lie point symmetries and Prelle-Singer procedure we construct a time independent integral for the case exhibiting maximal symmetry from which we identify the associated conservative non-standard Lagrangian and Hamiltonian functions. The classical dynamics of the nonlinear oscillator is also discussed and certain special properties including isochronous oscillations are brought out.Keywords Inverse problem · Liénard type nonlinear oscillator equation · Jacobi last multiplier · Prelle-Singer procedure · Lie point symmetries IntroductionIn general, the Lagrangian of an autonomous dynamical system is defined as the difference between kinetic and potential energies [1,2,3]. Systems which have Lagrangians of this form are termed as natural/standard Lagrangians. However, recent studies reveal that certain autonomous dynamical systems do admit other forms of Lagrangians in which no such clear identification of kinetic and potential energy terms can be made. In other words these new forms of Lagrangians do not have separate kinetic or potential energy terms. However, they provide the same equation of motion as

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confidence: 99%

The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective

et al. 2016

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“…Using this fact and solving Eq. (2.10), we can obtain the Darboux polynomials (F ) and the cofactors (g), see Mohanasubha et al (2014a) for further details on the method.…”

Section: (B) Darboux Polynomials Approachmentioning

confidence: 99%

“…Note also that for a given F, and an integral I of (2.1), the quantity f (I)F, where f is arbitrary, is also a solution of (2.10) for the same cofactor. Using this fact and solving equation (2.10), we can obtain the Darboux polynomials (F) and the cofactors (g); see Mohanasubha et al [8] for further details on the method.…”

Section: (B) Darboux Polynomials Approachmentioning

confidence: 99%

Interconnections between various analytic approaches applicable to third-order nonlinear differential equations

et al. 2015

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We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ODEs. We establish an important interconnection between the extended Prelle-Singer procedure and λ-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjointsymmetries, λ-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples.

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Finding non-local and contact/dynamical symmetries of Riccati chain

et al. 2023

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On the linearization of isochronous centre of a modified Emden equation with linear external forcing

Cited by 6 publications

References 27 publications

The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective

The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective

Interconnections between various analytic approaches applicable to third-order nonlinear differential equations

Finding non-local and contact/dynamical symmetries of Riccati chain

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