2D Novel Structures Along an Optical Fiber

Abstract

By using spectral methods, we present seven classes of stable and unstable structures that occur in a dissipative media. By varying parameters and initial conditions we find ranges of existence of stable structures (spinning elliptic, pulsating, stationary, organized exploding), and unstable structures (filament, disorganized exploding, creeping). By varying initial conditions, vorticity, and parameters of the equation, we find a reacher behavior of solutions in the form of creeping-vortex (propellers), spinning rings and spinning “bean-shape” solitons. Each class differentiates from the other by distinctive features of their shape and energy evolution, as well as domain of existence.