Riccati generalization of self-similar solutions of nonautonomous Gross-Pitaevskii equation
1 Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia, 741252, India
2 Department of Physics, Panjab University, Chandigarh 160014, India
Revised: 3 May 2013
Published online: 11 July 2013
We present a systematic analytical approach to construct a family of self-similar waves, related through a free parameter, in quasi one-dimension Gross-Pitaevskii equation with time-varying parameters. This approach enables us to control the dynamics of dark and bright similaritons, and first- and second- order self-similar rogue waves in Bose-Einstein condensate through the modulation of time dependent trapping potential. The analysis is done for the sech2− type time-varying quadratic trapping potential for two different choices of linear potential.
© EDP Sciences, Springer-Verlag, 2013