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Original Articles

Extended Prelle-Singer Method and Integrability/Solvability of a Class of Nonlinear nth Order Ordinary Differential Equations

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Pages 184-201 | Published online: 21 Jan 2013

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Gülden Gün Polat & Teoman Özer. (2023) Analytical approaches for growth models in economics. Quaestiones Mathematicae 46:12, pages 2529-2562.
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A Ghose Choudhury, Partha Guha & Barun Khanra. (2008) Solutions of some second order ODEs by the extended Prelle-Singer method and symmetries. Journal of Nonlinear Mathematical Physics 15:4, pages 365-382.
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Articles from other publishers (21)

Mohanasubha Ramasamy, Subhasri Devarajan, Senthilvelan Murugaian & Karthikeyan Rajagopal. (2023) On exploring $$\lambda $$-symmetries, Darboux polynomials and other integrable quantifiers of Easter Island Population Model. Pramana 97:3.
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R Mohanasubha & M Senthilvelan. (2023) A study on Darboux polynomials and their significance in determining other integrability quantifiers: A case study in third-order nonlinear ordinary differential equations. Pramana 97:1.
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Argha Mondal, Kshitish Ch. Mistri, M.A. Aziz-Alaoui & Ranjit Kumar Upadhyay. (2021) An analytical scheme on complete integrability of 2D biophysical excitable systems. Physica A: Statistical Mechanics and its Applications 573, pages 125924.
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Gülden GÜN POLAT. (2019) Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu. International Journal of Advances in Engineering and Pure Sciences 31:1, pages 62-69.
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R. Mohanasubha, V.K. Chandrasekar, M. Senthilvelan & M. Lakshmanan. (2018) On the interconnections between various analytic approaches in coupled first-order nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation 62, pages 213-228.
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Gülden Gün Polat & Teoman Özer. (2017) New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation. Journal of Computational and Nonlinear Dynamics 12:4.
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R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan & M. Lakshmanan. (2016) Interplay of symmetries and other integrability quantifiers in finite-dimensional integrable nonlinear dynamical systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472:2190, pages 20150847.
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P. R. Gordoa, A. Pickering & M. Senthilvelan. (2014) The Prelle-Singer method and Painlevé hierarchies. Journal of Mathematical Physics 55:5.
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J. Avellar, L.G.S. Duarte & L.A.C.P. da Mota. (2014) A Maple package to find first order differential invariants of 2ODEs via a Darboux approach. Computer Physics Communications 185:1, pages 307-316.
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M. Lakshmanan & V. K. Chandrasekar. (2013) Generating finite dimensional integrable nonlinear dynamical systems. The European Physical Journal Special Topics 222:3-4, pages 665-688.
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Lou Zhi-Mei & Mei Feng-Xiang. (2012) The third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator. Acta Physica Sinica 61:11, pages 110201.
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R. Gladwin Pradeep, V. K. Chandrasekar, M. Senthilvelan & M. Lakshmanan. (2010) On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka–Volterra system. Journal of Mathematical Physics 51:3.
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Lou Zhi-Mei. (2010) Finding conserved quantities of three-dimensional second-order nonlinear coupled dynamics systems by the extended Prelle-Singer method. Acta Physica Sinica 59:6, pages 3633.
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A. Ghose Choudhury, Partha Guha & Barun Khanra. (2009) On the Jacobi Last Multiplier, integrating factors and the Lagrangian formulation of differential equations of the Painlevé–Gambier classification. Journal of Mathematical Analysis and Applications 360:2, pages 651-664.
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C Muriel & J L Romero. (2009) First integrals, integrating factors and λ-symmetries of second-order differential equations. Journal of Physics A: Mathematical and Theoretical 42:36, pages 365207.
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José F Cariñena, Partha Guha & Manuel F Rañada. (2009) A geometric approach to higher-order Riccati chain: Darboux polynomials and constants of the motion. Journal of Physics: Conference Series 175, pages 012009.
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R Gladwin Pradeep, V K Chandrasekar, M Senthilvelan & M Lakshmanan. (2009) Dynamics of a completely integrable N -coupled Liénard-type nonlinear oscillator . Journal of Physics A: Mathematical and Theoretical 42:13, pages 135206.
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Partha Guha, A Ghose Choudhury & Barun Khanra. (2009) On adjoint symmetry equations, integrating factors and solutions of nonlinear ODEs. Journal of Physics A: Mathematical and Theoretical 42:11, pages 115206.
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V K Chandrasekar, M Senthilvelan & M Lakshmanan. (2008) Reply to ?Comment on ?On the general solution for the modified Emden type equation \ddot{x}+\alpha x\dot{x}+\beta x^3=0 ??. Journal of Physics A: Mathematical and Theoretical 41:6, pages 068002.
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V. K. Chandrasekar, S. N. Pandey, M. Senthilvelan & M. Lakshmanan. (2006) A simple and unified approach to identify integrable nonlinear oscillators and systems. Journal of Mathematical Physics 47:2.
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José F. Cariñena, Manuel F. Rañada & Mariano Santander. (2005) Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability. Journal of Mathematical Physics 46:6.
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