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| Dispersive Blow-Up II. Schr¨odinger-Type Equations,Optical and Oceanic Rogue Waves |
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Citation： |
Jerry L. BONA,Jean-Claude SAUT.Dispersive Blow-Up II. Schr¨odinger-Type Equations,Optical and Oceanic Rogue Waves[J].Chinese Annals of Mathematics B,2010,31(6):793~818 |
| Page view： 2206
Net amount： 1266 |
Authors： |
Jerry L. BONA; Jean-Claude SAUT; |
Foundation： |
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 Universit′e de Paris 11. |
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| 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 Schrodinger equations, a class of
fractional order Schrodinger 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
Schrodinger equation, Water wave equations, Propagation in optical cables,
Weak turbulence models |
Classification： |
35Q35, 35Q51, 35Q53, 35Q55, 35Q60, 35Q86,
76B03, 76B15, 76B45, 76F99, 78A60 |
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