1,605 research outputs found
Matter wave switching in Bose-Einstein condensates via intensity redistribution soliton interactions
Using time dependent nonlinear (s-wave scattering length) coupling between
the components of a weakly interacting two component Bose-Einstein condensate
(BEC), we show the possibility of matter wave switching (fraction of atoms
transfer) between the components via shape changing/intensity redistribution
(matter redistribution) soliton interactions. We investigate the exact
bright-bright N-soliton solution of an effective one-dimensional (1D) two
component BEC by suitably tailoring the trap potential, atomic scattering
length and atom gain or loss. In particular, we show that the effective 1D
coupled Gross-Pitaevskii (GP) equations with time dependent parameters can be
transformed into the well known completely integrable Manakov model described
by coupled nonlinear Schr\"odinger (CNLS) equations by effecting a change of
variables of the coordinates and the wave functions under certain conditions
related to the time dependent parameters. We obtain the one-soliton solution
and demonstrate the shape changing/matter redistribution interactions of two
and three soliton solutions for the time independent expulsive harmonic trap
potential, periodically modulated harmonic trap potential and kink-like
modulated harmonic trap potential. The standard elastic collision of solitons
occur only for a specific choice of soliton parameters.Comment: 11 pages, 14 figures, 1 tabl
Estimation of System Parameters in Discrete Dynamical Systems from Time Series
We propose a simple method to estimate the parameters involved in discrete
dynamical systems from time series. The method is based on the concept of
controlling chaos by constant feedback. The major advantages of the method are
that it needs a minimal number of time series data and is applicable to
dynamical systems of any dimension. The method also works extremely well even
in the presence of noise in the time series. The method is specifically
illustrated by means of logistic and Henon maps.Comment: 4 page
Estimation of System Parameters and Predicting the Flow Function from Time Series of Continuous Dynamical Systems
We introduce a simple method to estimate the system parameters in continuous
dynamical systems from the time series. In this method, we construct a modified
system by introducing some constants (controlling constants) into the given
(original) system. Then the system parameters and the controlling constants are
determined by solving a set of nonlinear simultaneous algebraic equations
obtained from the relation connecting original and modified systems. Finally,
the method is extended to find the form of the evolution equation of the system
itself. The major advantage of the method is that it needs only a minimal
number of time series data and is applicable to dynamical systems of any
dimension. The method also works extremely well even in the presence of noise
in the time series. This method is illustrated for the case of Lorenz system.Comment: 12 pages, 4 figure
A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term
The properties of a nonlinear oscillator with an additional term ,
characterizing the isotonic oscillator, are studied. The nonlinearity affects
to both the kinetic term and the potential and combines two nonlinearities
associated to two parameters, and , in such a way that for
all the characteristics of of the standard isotonic system are
recovered. The first part is devoted to the classical system and the second
part to the quantum system. This is a problem of quantization of a system with
position-dependent mass of the form , with a
-dependent non-polynomial rational potential and with an additional
isotonic term. The Schr\"odinger equation is exactly solved and the
-dependent wave functions and bound state energies are explicitly
obtained for both .Comment: two figure
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