Article
Stability analysis of orbital modes for a generalized Lane-Emden equation
Communications in Nonlinear Science and Numerical Simulation
(2018)
Abstract
We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial distributions of magnetically-trapped ultracold atomic clouds. A Lyapunov function is defined which helps us to prove that stable spatial structures in the atomic clouds exist only for adiabatic index γ=1+1/n with even n. In the case when n is odd we provide an instability result indicating the divergence of the density function for the atoms. Several numerical solutions, which according to our stability analysis are stable, are also presented.
Disciplines
Publication Date
Summer August 6, 2018
DOI
10.1016/j.cnsns.2018.08.001
Citation Information
Ronald Adams, S. C. Mancas and Haret C. Rosu. "Stability analysis of orbital modes for a generalized Lane-Emden equation" Communications in Nonlinear Science and Numerical Simulation (2018) ISSN: 1007-5704 Available at: http://works.bepress.com/stefani_mancas/75/