General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find; although, powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases particular solutions may be found with little effort if it is possible to factorize the equation in terms of first-order differential operators. In our present study, we use this factorization technique to address the problem of finding solutions of a system of general two-coupled Liénard-type nonlinear differential equations. We describe a generic algorithm to identify specific classes of Liénard-type systems for which solutions may be found. We demonstrate this method by identifying a class of two-coupled equations for which the particular solution can be found by solving a Bernoulli equation. This class of equations include coupled generalization of the modified Emden equation. We further deduce the general solution of a class of coupled ODEs using the factorization procedure discussed in this paper.
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February 2012
Research Article|
February 15 2012
Exact solutions of coupled Liénard-type nonlinear systems using factorization technique
Tamaghna Hazra;
Tamaghna Hazra
1Department of Physics,
Indian Institute of Technology Kanpur
, Kanpur 208016, India
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V. K. Chandrasekar;
V. K. Chandrasekar
2Centre for Nonlinear Dynamics, Department of Physics,
Bharathidasan University
, Tiruchirappalli 620 024, India
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R. Gladwin Pradeep;
R. Gladwin Pradeep
2Centre for Nonlinear Dynamics, Department of Physics,
Bharathidasan University
, Tiruchirappalli 620 024, India
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M. Lakshmanan
M. Lakshmanan
a)
2Centre for Nonlinear Dynamics, Department of Physics,
Bharathidasan University
, Tiruchirappalli 620 024, India
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a)
Electronic mail: [email protected].
J. Math. Phys. 53, 023511 (2012)
Article history
Received:
November 28 2011
Accepted:
January 24 2012
Citation
Tamaghna Hazra, V. K. Chandrasekar, R. Gladwin Pradeep, M. Lakshmanan; Exact solutions of coupled Liénard-type nonlinear systems using factorization technique. J. Math. Phys. 1 February 2012; 53 (2): 023511. https://doi.org/10.1063/1.3684956
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