Geometry and control of three-wave interactions

Geometry and control of three-wave interactions (1997)

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by Mark S. Alber , Gregory G. Luther , Jerrold E. Marsden , Jonathan M. Robbins

Venue:	in The Arnoldfest
Citations:	4 - 1 self

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Datum	Value	Source
TITLE	Geometry and control of three-wave interactions	INFERENCE
AUTHOR NAME	Mark S. Alber	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of Mathematics; University of Notre Dame	SVM HeaderParse 0.2
AUTHOR ADDR	Notre Dame, IN 46556	SVM HeaderParse 0.2
AUTHOR NAME	Gregory G. Luther	SVM HeaderParse 0.2
AUTHOR AFFIL	Engineering Sciences and Applied Mathematics Department; McCormick School of Engineering and Applied Science; Northwestern University	SVM HeaderParse 0.2
AUTHOR ADDR	2145 Sheridan Road; Evanston, Il 60208–3125.	SVM HeaderParse 0.2
AUTHOR NAME	Jerrold E. Marsden	SVM HeaderParse 0.2
AUTHOR AFFIL	Control and Dynamical Systems 107-81; Caltech,	SVM HeaderParse 0.2
AUTHOR ADDR	Pasadena, CA 91125	SVM HeaderParse 0.2
AUTHOR NAME	Jonathan M. Robbins	SVM HeaderParse 0.2
AUTHOR AFFIL	; The Basic Research Institute in the Mathematical Sciences (BRIMS); Hewlett-Packard Laboratories; and; School of Mathematics; University Walk, Bristol	SVM HeaderParse 0.2
AUTHOR ADDR	; Filton Road, Stoke Gifford; Bristol BS12 6QZ, UK; BS8 1TW UK	SVM HeaderParse 0.2
ABSTRACT	The integrable structure of the three-wave equations is discussed in the setting of geometric mechanics. Lie-Poisson structures with quadratic Hamiltonian are associated with the three-wave equations through the Lie algebras su(3) and su(2, 1). A second structure having cubic Hamiltonian is shown to be compatible. The analogy between this system and the rigid-body or Euler equations is discussed. Poisson reduction is performed using the method of invariants and geometric phases associated with the reconstruction are calculated. We show that using piecewise continuous controls, the transfer of energy among three 1 waves can be controlled. The so called quasi-phase-matching control strategy, which is used in a host of nonlinear optical devices to convert laser light from one frequency to another, is described in this context. Finally, we discuss the connection between piecewise constant controls and billiards.	SVM HeaderParse 0.2
YEAR	1997	INFERENCE
VENUE	in The Arnoldfest	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	55--80	INFERENCE
VOLUME	24	INFERENCE
CITATIONS	40 found	ParsCit 1.0