Eur. Phys. J. Plus (2016) 131: 66
https://doi.org/10.1140/epjp/i2016-16066-x

Regular Article

Shock waves in quasi one-dimensional Bose-Einstein condensate

¹ Dipartimento di Fisica “Galileo Galilei” and CNISM, Università di Padova, Via Marzolo 8, 35131, Padova, Italy
² CNR-INO, Via Nello Carrara 1, 50019, Sesto Fiorentino, Italy

^* e-mail: luca.salasnich@unipd.it

Received: 13 December 2015
Accepted: 2 February 2016
Published online: 28 March 2016

Abstract

We study analytically and numerically the generation of shock waves in a quasi-one-dimensional Bose-Einstein condensate (BEC) made of dilute and ultracold alkali-metal atoms. For the BEC we use an equation of state based on a 1D nonpolynomial Schrödinger equation (1D NPSE), which takes into account density modulations in the transverse direction and generalizes the familiar 1D Gross-Pitaevskii equation (1D GPE). Comparing 1D NPSE with 1D GPE we find quantitative differences in the dynamics of shock waves regarding the velocity of propagation, the time of formation of the shock, and the wavelength of after-shock dispersive ripples.