Rogue waves of the vector nonlinear Schrödinger equations

Abstract

Summary form only given. Extreme wave events, also referred to as freak or rogue waves, are mostly known as oceanic phenomena responsible for a large number of maritime disasters. These waves, which have height and steepness much greater than expected from the sea average state [1], have recently become a topic of intense research. Rogue waves appear both in deep ocean and in shallow water [2]. Research on rogue waves is in an emerging state [1,3]. These waves not only appear in oceans but also in the atmosphere, in optics, in plasmas, in superfluids, in Bose-Einstein condensates and also as capillary waves. The common features and differences among freak wave manifestations in their different contexts is a subject of intense discussion [2]. A formal mathematical description of a rogue wave is provided by the so-called Peregrine soliton [4]. This solitary wave is a solution of the 1 + 1 scalar Nonlinear Schrodinger Equation (NLSE) with the property of being localized in both coordinates. Recent experiments have provided a path to generating Peregrine solitons in optical fibers with standard telecommunication equipment [5]. The further experimental observation of Peregrine solitons in a water tank [6] indicates that they can also describe rogue waves in oceans. However, in a variety of complex systems such as Bose-Einstein condensates, optical fibers, and financial systems, several amplitudes rather than a single one need to be considered. The resulting systems of coupled equations may thus describe extreme waves with higher accuracy than the scalar NLSE model. Approaches to rogue wave phenomena involving more than one wave amplitude are the Gross-Pitaevskii (GP) model and the Vector Nonlinear Schrodinger Equations (VNLSE) or Manakov system. We will show our contribution to the Ield of rogue waves by presenting new multi-parametric vector soliton solutions of the Manakov system which extend the results we have recently reported in [7]. This family of solutions includes known vector Peregrine solutions, bright-dark-rogue solutions, accelerating boomeroninc structures, and vector unusual rogue dynamics (as an example, Fig. 1 shows the generation of one rogue wave out of a slowly moving boomeronic breather). Moreover, we discuss the experimental conditions for the observation of our vector, semirational rogue solitons considering i) the propagation of polarized picosecond pulses in randomly birefringent optical fibers and ii) incoherently coupled photorefractive spatial waves in strontium barium borate (SBN).