Chandrasekar, V. K. ; Senthilvelan, M. ; Lakshmanan, M. (2007) On the general solution for the modified Emden-type equation x.. + αxx. + βx3 = O Journal of Physics A: Mathematical and Theoretical, 40 (18). pp. 4717-4727. ISSN 1751-8113
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Official URL: http://iopscience.iop.org/1751-8121/40/18/003
Related URL: http://dx.doi.org/10.1088/1751-8113/40/18/003
Abstract
In this paper, we demonstrate that the modified equation of Emden type (MEE), x.. + αxx. + βx3 = 0, is integrable either explicitly or by quadrature for any value of α and β . We also prove that the MEE possesses appropriate time-independent Hamiltonian functions for the full range of parameters α and β. In addition we show that the MEE is intimately connected with two well-known nonlinear models, namely the equation of force-free Duffing-type oscillator and the two-dimensional Lotka-Volterra equation, and thus the complete integrability of the latter two models can also be understood in terms of the MEE.
| Item Type: | Article |
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| Source: | Copyright of this article belongs to Institute of Physics Publishing. |
| ID Code: | 19555 |
| Deposited On: | 22 Nov 2010 12:24 |
| Last Modified: | 17 May 2016 04:05 |
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