On the general solution for the modified Emden type equation $\ddot{x}+αx\dot{x}+βx^3=0$
| dc.creator | Chandrasekar, V K | |
| dc.creator | Senthilvelan, M | |
| dc.creator | Lakshmanan, M | |
| dc.date | 2006-11-22 | |
| dc.date.accessioned | 2026-07-07T07:33:37Z | |
| dc.date.available | 2026-07-07T07:33:37Z | |
| dc.description | In this paper, we demonstrate that the modified Emden type equation (MEE), $\ddot{x}+αx\dot{x}+βx^3=0$, 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 function 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 force-free Duffing type oscillator equation and the two dimensional Lotka-Volterra (LV) equation and thus the complete integrability of the latter two models can also be understood in terms of the MEE. | |
| dc.description | 12 pages, one figure | |
| dc.identifier | https://arxiv.org/abs/nlin/0611043 | |
| dc.identifier | http://arxiv.org/abs/nlin/0611043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119524 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | On the general solution for the modified Emden type equation $\ddot{x}+αx\dot{x}+βx^3=0$ | |
| dc.type | text |