V. Ramesh Kumar

Remote controlling the dynamics of Bose-Einstein condensates through time-dependent atomic feeding and trap

In this paper, we generate the Lax pair of the nonconservative Gross?Pitaevskii (GP) equation with time-dependent linear and harmonic oscillator potentials and construct a multisoliton solution using gauge transformation. We show how an interplay between the dispersion coefficient, scattering length and atomic feeding can suitably be exploited to remote control the dynamics of solitons, thereby generating favorable profiles of Bose?Einstein condensates (BECs), notable among them being the matter wave similaritons.

Line-soliton dynamics and stability of Bose–Einstein condensates in (2+1) Gross–Pitaevskii equation

We investigate the (2+1)-dimensional Gross–Pitaevskii equation in an isotropic expulsive harmonic trap and generate bright line solitons for the condensates by employing the Hirota method. We observe that one can increase the density of the condensates (or line solitons) by suitably tuning the trap frequency even for constant scattering lengths. The two line-soliton dynamics indicate the occurrence of an instability in the condensates once the density exceeds a critical value. This instability could possibly be overcome by the addition of suitable dissipation which subsequently increases the lifespan of the condensates.

Gauge equivalence of the Gross–Pitaevskii equation and the equivalent Heisenberg spin chain

In this paper, we construct an equivalent spin chain for the Gross–Pitaevskii equation with quadratic potential and exponentially varying scattering lengths using gauge equivalence. We have then generated the soliton solutions for the spin components S3 and S−. We find that the spin solitons for S3 and S− can be compressed for exponentially growing eigenvalues while they broaden out for decaying eigenvalues.