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
