Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) in D-dimensions

Spherically symmetric oscillatons (also referred to as oscillating soliton stars) i.e. gravitationally bound oscillating scalar lumps are considered in theories containing a massive self-interacting real scalar field coupled to Einstein's gravity in 1+D dimensional spacetimes. Oscillations are known to decay by emitting scalar radiation with a characteristic time scale which is, however, extremely long, it can be comparable even to the lifetime of our universe. In the limit when the central density (or amplitude) of the oscillaton tends to zero (small-amplitude limit) a method is introduced to compute the transcendentally small amplitude of the outgoing waves. The results are illustrated in detail on the simplest case, a single massive free scalar field coupled to gravity.Comment: 23 pages, 2 figures, references on oscillons added, version to appear in Phys. Rev.

Small amplitude quasi-breathers and oscillons

Quasi-breathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006). QB's provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QB's is worked out in a large class of scalar theories with a general self-interaction potential, in $D$ spatial dimensions. It is shown that the problem of small amplitude QB's is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, $D_{crit}=4$, above which no small amplitude QB's exist. The QB's obtained this way are shown to provide very good initial data for oscillons. Thus these QB's provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.Comment: 24 pages, 19 figure

AKNS and NLS hierarchies, MRW solutions, PnP_n breathers, and beyond

International audienceWe describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrödinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and rank-3 quasi-rational solutions that can be used for prediction and modeling of the rogue wave events in fiber optics, hydrodynamics, and many other branches of science