摘要
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 Schrdinger equations, a class of fractional order Schrdinger 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.
基金
supported by the Agence Nationale de la Recherche, France (No. ANR-07-BLAN-0250)
the University of Illinois at Chicago,the Wolfgang Pauli Institute in Vienna, the University of Illinois at Chicago and the Université de Paris 11
