195 citations · 1.8k across the 115 of their papers we have counts for
39 papers · 1 filter
Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System
C. Uma Maheswari, N. Muthuchamy, V. K. Chandrasekar +2
We consider a modified damped version of Hénon-Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that t…
A Class of Isochronous and Non-Isochronous Nonlinear Oscillators
J. Ramya Parkavi, R. Mohanasubha, V. K. Chandrasekar +2
In this work, we present a method of generating a class of nonlinear ordinary differential equations (ODEs), representing the dynamics of appropriate nonlinear oscillators, that ha…
A note on deriving linearizing transformations for a class of second order nonlinear ordinary differential equations
R Mohanasubha, V. K. Chandrasekar, M. Senthilvelan
We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordina…
Two-dimensional isochronous nonstandard Hamiltonian systems
A. Durga Devi, R. Gladwin Pradeep, V. K. Chandrasekar +1
We identify a generic class of two dimensional nonstandard Hamiltonian systems which exhibit isochronous behaviour. This class of systems belongs to the two dimensional mixed Liéna…
Interplay of symmetries and other integrability quantifiers in finite dimensional integrable nonlinear dynamical systems
R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan +1
In this work, we establish a connection between the extended Prelle-Singer procedure with other widely used analytical methods to identify integrable systems in the case of $n^{th}…
The inverse problem of a mixed Liénard type nonlinear oscillator equation from symmetry perspective
Ajey K. Tiwari, S. N. Pandey, V. K. Chandrasekar +2
In this paper, we discuss the inverse problem for a mixed Liénard type nonlinear oscillator equation , where and are…
Symmetries of nonlinear ordinary differential equations: the modified Emden equation as a case study
M. Senthilvelan, V. K. Chandrasekar, R. Mohanasubha
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries.…
On certain analytical methods in finding integrable systems and their interconnections
R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan +1
In this paper, to begin with, we review six different analytical methods which are widely used to derive symmetries, integrating factors, multipliers, Darboux polynomials and integ…
Interconnections between various analytic approaches applicable to third-order nonlinear differential equations
R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan +1
We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by th…
Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains
R. Gladwin Pradeep, V. K. Chandrasekar, R. Mohanasubha +2
We identify contact transformations which linearize the given equations in the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations to the same o…
Factorization technique and isochronous condition for coupled quadratic and mixed Liénard-type nonlinear systems
Ajey K. Tiwari, V. K. Chandrasekar, S. N. Pandey +1
In this paper, we discuss a systematic and self consistent procedure to factorize a rather general class of coupled nonlinear ordinary differential equations (ODEs), namely coupled…
Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second order differential equations
R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan +1
In this work, we establish a connection between the extended Prelle-Singer procedure (Chandrasekar \textit{et al.} Proc. R. Soc. A 2005) with five other analytical methods which ar…
A nonlocal connection between certain linear and nonlinear ordinary differential equations - Part II: Complex nonlinear oscillators
R. Mohanasubha, Jane H. Sheeba, V. K. Chandrasekar +2
In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal t…
Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
M. Lakshmanan, V. K. Chandrasekar
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting…
On the complete integrability of a nonlinear oscillator from group theoretical perspective
A. Bhuvaneswari, V. K. Chandrasekar, M. Senthilvelan +1
In this paper, we investigate the integrability aspects of a physically important nonlinear oscillator which lacks sufficient number of Lie point symmetries but can be integrated b…
Method of generating -dimensional isochronous nonsingular Hamiltonian systems
A. Durga Devi, R. Gladwin Pradeep, V. K. Chandrasekar +1
In this paper we develop a straightforward procedure to construct higher dimensional isochronous Hamiltonian systems. We first show that a class of singular Hamiltonian systems obt…
A class of solvable coupled nonlinear oscillators with amplitude independent frequencies
V. K. Chandrasekar, Jane H. Sheeba, R. Gladwin Pradeep +2
Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillator…
Exact solutions of coupled Liénard-type nonlinear systems using factorization technique
Tamaghna Hazra, V. K. Chandrasekar, R. Gladwin Pradeep +1
General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this p…
A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: II. Extension to coupled ODEs
V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan
In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second order nonlinear ODEs. We show tha…
Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order
R. Gladwin Pradeep, V. K. Chandrasekar, M. Senthilvelan +1
In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to lin…
A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: I. Scalar case
V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan
In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order in…
A nonlocal connection between certain linear and nonlinear ordinary differential equations : Extension to coupled equations
R. Gladwin Pradeep, V. K. Chandrasekar, M. Senthilvelan +1
Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlin…
Recursive Generation of Isochronous Hamiltonian Systems
V. K. Chandrasekar, A. Durga Devi, M. Lakshmanan
We propose a simple procedure to identify the collective coordinate which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and mo…
On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system
R. Gladwin Pradeep, V. K. Chandrasekar, M. Senthilvelan +1
In this paper, we consider a second order nonlinear ordinary differential equation of the form , where …