Eur. Phys. J. Special Topics 222, 655-663 (2013)
https://doi.org/10.1140/epjst/e2013-01870-7

Regular Article

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

^a e-mail: pprasanta@iiserkol.ac.in
^b e-mail: cnkumar@pu.ac.in

Received: 22 March 2013
Revised: 3 May 2013
Published online: 11 July 2013

Abstract

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.