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Estimates for the three-wave interaction of surface water waves

Published online by Cambridge University Press:  24 October 2003

GUIDO SCHNEIDER
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany email: guido.schneider@mathematik.uni-karlsruhe.de
C. EUGENE WAYNE
Affiliation:
Department of Mathematics and Center for BioDynamics, Boston University, Cummington St., Boston, MA 02215, USA email: cew@math.bu.edu

Abstract

The equations for three-wave interaction describe the resonant, quadratic, nonlinear interaction of three waves. They are obtained as amplitude equations in an asymptotic reduction of the basic equations of nonlinear optics, fluid mechanics, and plasma physics. These equations are completely integrable and have been the subject of intensive research in the last years. It is the purpose of this paper to prove exact estimates between the approximations obtained via this system and solutions of the original physical system. Although the three-wave interaction model is believed to describe a number of different physical models we restrict attention to its application as a model of the resonant interaction of water waves subject to weak surface tension.

Type
Papers
Copyright
© 2003 Cambridge University Press

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