Dispersive blow-up II. Schrödinger-type equations, optical and oceanic rogue waves

Abstract

Addressed here is the occurrence of point singularities which owe to the focusing of short or long waves, a phenomenon labeled dispersive blow-up. The context of this investigation is linear and nonlinear, strongly dispersive equations or systems of equations. The present essay deals with linear and nonlinear Schrödinger equations, a class of fractional order Schrödinger equations and the linearized water wave equations, with and without surface tension. Commentary about how the results may bear upon the formation of rogue waves in fluid and optical environments is also included.

Keywords

Rogue waves / Dispersive blow-up / Nonlinear dispersive equations / Nonlinear Schrödinger equation / Water wave equations / Propagation in optical cables / Weak turbulence models

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