https://doi.org/10.1140/epjp/s13360-020-00648-6
Regular Article
Nonlinear Schrödinger equations involved in dark matter halos: modulational instability
1
Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, B. P. 32, El Alia, 16111, Algiers, Algeria
2
Department of Mathematics and Physics, Faculty of Science, Kanagawa University, 2946, 6-233 Tsuchiya, 259-1293, Hiratsuka, Kanagawa, Japan
Received:
10
March
2020
Accepted:
28
July
2020
Published online:
7
August
2020
Inspired by the theory of scale relativity, a nonlinear Schrödinger equation has been recently proposed to model dark matter halos. The equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Herein, we study the Benjamin–Feir type modulational instability exhibited by this model. We extend our analysis to further generalizations of the equation in the presence of short-range interactions, giving rise to Gross–Pitaevskii-like and Cahn–Hilliard-like equations, as well as to a generalization emerging from the Lynden–Bell distribution. In each case, we establish a criterion leading to modulational instability and study the corresponding growth rate.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
