Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Interaction of two quasi-monochromatic waves in shallow water Dipartimento di Fisica Generale, Universita` di Torino, via Pietro Giuria 1, 10125 Torino, Italy
 

Summary: Interaction of two quasi-monochromatic waves in shallow water
M. Onorato
Dipartimento di Fisica Generale, Universita` di Torino, via Pietro Giuria 1, 10125 Torino, Italy
D. Ambrosi
Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
A. R. Osborne and M. Serio
Dipartimento di Fisica Generale, Universita` di Torino, via Pietro Giuria 1, 10125 Torino, Italy
Received 16 July 2003; accepted 1 September 2003; published 6 November 2003
We study the nonlinear interaction of waves propagating in the same direction in shallow water
characterized by a double-peaked power spectrum. The starting point is the prototypical equation for
weakly nonlinear unidirectional waves in shallow water, i.e., the Korteweg­de Vries equation. In
the framework of envelope equations, using a multiple-scale technique and under the hypothesis of
narrow-banded spectra, a system of two coupled nonlinear Schro¨dinger equations is derived. The
validity of the resulting model and the stability of their plane wave solutions is discussed. We show
that when retaining higher order dispersive terms in the system, plane wave solutions become
modulationally unstable. © 2003 American Institute of Physics. DOI: 10.1063/1.1622394
The propagation of multiple wave-train systems in shal-
low water has historically received less attention than the
propagation of one single wave train. Nevertheless, experi-
mental studies carried out by Thompson1

  

Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino

 

Collections: Mathematics