Eur. Phys. J. Plus (2018) 133: 51
https://doi.org/10.1140/epjp/i2018-11877-3

Regular Article

Dissipative nonlinear waves in a gravitating quantum fluid

¹ Department of Mathematics, West Bengal State University, Barasat, 700126, Kolkata, India
² Physics and Applied Mathematics Unit, Indian Statistical Institute, 700108, Kolkata, India
³ Department of Mathematics, Bethune College, 181 Bidhan Sarani, 700006, Kolkata, India

^* e-mail: sinha.anjana@gmail.com

Received: 20 October 2017
Accepted: 15 January 2018
Published online: 14 February 2018

Abstract

Nonlinear wave propagation is studied in a dissipative, self-gravitating Bose-Einstein condensate, starting from the Gross-Pitaevskii equation. In the absence of an exact analytical result, approximate methods like the linear analysis and perturbative approach are applied. The linear dispersion relation puts a restriction on the permissible range of the dissipation parameter. The waves get damped due to dissipation. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation, which is solved both analytically as well as numerically. Interestingly, the analytical and numerical plots match excellently with each other, in the realm of weak dissipation.