Volumes of second-order rogue waves of the infinite NLS hierarchy

Abstract

We analyze first- and second-order rogue waves of the equations in the nonlinear Schrödinger equation (NLS) hierarchy. A physical phenomenon may be described by an individual equation or by a combination of them. We focus on localized (in 2D) formations. Then we can find the ‘volumes’ of these rogue waves and classify the formations as rogue or ‘semi-rogue’ waves. In other cases, there can be a rogue-type central structure connected to ‘soliton tails,’ and, in these cases, the standard ‘volume’ may be infinite, and a ’modified volume’ can be introduced. Show more