We study the periodic cubic derivative non-linear Schr\"odinger equation (dNLS) and (focussing) quintic (NLS). These are both $L^2$ critical dispersive models, which exhibit threshold type behavior, when posed on line ${\mathbb R}$. describe (three parameter) family of non-vanishing bell-shaped solutions for problem, in closed form. The main objective paper is to their stability with respect co...

We study the imprints of secluded dark sectors with a mass gap and self-interactions on matter power spectrum. When Dark Matter (DM) is sufficiently light, in ballpark few KeV, self-interacting we find qualitative difference respect to $\Lambda$CDM also free streaming DM. In order emphasize role interactions for evolution primordial perturbations discuss various regimes: ranging from ideal case...

One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In th...

We analyse an operator arising in the description of singular solutions to two-dimensional Keller-Segel problem. It corresponds linearised parabolic self-similar variables, close a concentrated stationary state. This is two-scale problem, with vanishing thin transition zone near origin. Via rigorous matched asymptotic expansions, we describe eigenvalues and eigenfunctions precisely. also show s...

A bstract In previous work, a first law of generalized entropy was derived from semiclassical gravitational dynamics around thermal setups using an assumed relation between the matter modular Hamiltonian and stress tensor. Allowing for non-minimal coupling curvature any tensor fields, we show however, that states is given by integrated bulk Noether current associated to time translation plus sp...

We study the asymptotic behavior of viscosity solutions uGλ Hamilton-Jacobi (HJ) equation λu(x)+G(x,u′)=c(G) in Ras positive discount factor λ tends to 0, where G(x,p):=H(x,p)−V(x) is perturbation a Hamiltonian H∈ C(R×R), Z–periodic space variable and convex coercive momentum, by compactly supported potential V∈Cc(R). The constant c(G) appearing above defined as infimum values a∈R for which HJ ...

We study the non–linear dynamics of self–gravitating irrotational dust in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. All the equations are written in terms of a single tensor variable, the metric tensor of the spatial sections orthogonal to the fluid flow. This treatment allows an unambiguous expansion in inverse (even) powers of the speed of...