Solitons and oscillons in scalar field theories

This talk will investigate localized field configurations – solitons and oscillons – in non-integrable scalar theories. First part of the talk addresses unusual properties of one-dimensional solitons in scalar theories with non-integrable static equations that exhibit chaos. In particular, we will consider the sine-Gordon model in external Dirac comb potential. It appears that the number of different stable solitons in this system grows exponentially with their length. Moreover, we will show that the field values of stable solitons form a fractal, we estimate its box-counting dimension. We will also discuss how statistical properties of static solitons are related to topological and metric entropies of the static equations. Second part of the talk will focus on oscillons – almost periodic extremely long-lived field lumps that exist in a plethora of scalar theories and may affect several cosmological scenarios. We will construct an effective field theory that describes them as nontopological solitons. Special attention will be given to the monodromy model with nearly quadratic potential which is capable of sustaining oscillons of gigantic amplitude and extreme longevity. We will obtain criteria for existence and longevity of oscillons in the effective theory, as well as their stability. Finally, we will discuss oscillons in the low-dimensional limit.