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The cold dark matter (CDM) paradigm provides a remarkably good description of the Universe's large-scale structure. However, some discrepancies exist between its predictions and observations at very small sub-galactic scales. To address…
We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms.…
Self-interacting dark matter (SIDM) has been proposed to address small-scale challenges faced by the cold dark matter (CDM) paradigm, such as the diverse density profiles observed in dwarf galaxies. In this study, we analyze the kinematics…
We elaborate a fractional discrete nonlinear Schr\"{o}dinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its L\'{e}vy index (LI). This FDNLS equation…
Non-gravitational interaction between two barotropic dark fluids, namely the pressureless dust and the dark energy in a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker model has been discussed. It is shown that for the interactions…
By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii…
We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrodinger equation. Our approach offers a systematic way of analyzing the existence and…
The Schr\"odinger-Newton equation is a proposed model to explain the localization of macroscopic particles by suppressing quantum dispersion with the particle's own gravitational attraction. On cosmic scales, however, dark energy also acts…
We study the formation of solitons inside scalar-field dark matter halos with a non-polynomial self-interaction potential. We consider a self-interaction potential that is quartic in the scalar field in the low-density regime but saturates…
We explore the consequences of including the repulsive three-particle interaction in the model of Bose-Einstein condensate dark matter model or fuzzy dark matter. Such a model based on properly modified Gross-Pitaevskii equation is intended…
Spatiotemporal patterns are often modeled using reaction-diffusion equations, which combine complex reactions between constituents with ideal diffusive motion. Such descriptions neglect physical interactions between constituents, which…
We derive non-relativistic equations of motion for the formation of cosmological structure in a Scalar Field Dark Matter (SFDM) model corresponding to a complex scalar field endowed with a quadratic scalar potential. Starting with the full…
Dark matter (DM) self-interactions have been proposed to solve problems on small length scales within the standard cold DM cosmology. Here, we investigate the effects of DM self-interactions in merging systems of galaxies and galaxy…
A pressureless dark matter component fits well with several cosmological observations. However, there are indications that cold dark matter may encounter challenges in explaining observations at small scales, particularly at galactic…
We study production of self-interacting dark matter (DM) during an early matter-dominated phase. As a benchmark scenario, we consider a model where the DM consists of singlet scalar particles coupled to the visible Standard Model (SM)…
We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected,…
One of the challenging questions in cosmology is the nature of dark matter particles. Fuzzy Dark Matter (FDM) is one of the candidates which is made of very light ($m_{FDM}\simeq 10^{-22}-10^{-21}$ eV) bosonic particles with no…
The Discrete NonLinear Schr\"odinger (DNLS) equation displays a parameter region characterized by the presence of localized excitations (breathers). While their formation is well understood and it is expected that the asymptotic…
Fuzzy dark matter (FDM), a scalar particle coupled to the gravitational field without self-interaction whose mass range is $m \sim 10^{-24} - 10^{-20}\ \rm{eV}$, is one of the promising alternative dark matter candidates to cold dark…
We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential.…