On the general solution for the modified Emden type equation $\ddot{x}+αx\dot{x}+βx^3=0$

dc.creatorChandrasekar, V K
dc.creatorSenthilvelan, M
dc.creatorLakshmanan, M
dc.date2006-11-22
dc.date.accessioned2026-07-07T07:33:37Z
dc.date.available2026-07-07T07:33:37Z
dc.descriptionIn 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.description12 pages, one figure
dc.identifierhttps://arxiv.org/abs/nlin/0611043
dc.identifierhttp://arxiv.org/abs/nlin/0611043
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119524
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn the general solution for the modified Emden type equation $\ddot{x}+αx\dot{x}+βx^3=0$
dc.typetext

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