DOI: 10.1088/0305-4470/34/21/305
WoS: 000169248700007
20 Citations
Résumé:

Nonlinear monochromatic short surface waves in ideal fluids are studied and, by the general consideration of wave dynamics and perturbative methods a simple and effective multiscale approach is devised for nonlinear asymptotic short-wave dynamics in dispersive systems. In particular the evolution of a monochromatic surface wave in an ideal fluid is shown to lead to a modified Green-Naghdi system of equations and a Green-Naghdi system with surface tension. Short surface waves exist in these systems and the nonlinear asymptotic analysis produces the nonlinear model equations that govern their dynamics. Particular solutions are shown. Moreover the method allows for a general classification of classical model equations as Boussinesq, Benjamin-Bona-Mahony-Peregrine and Camassa-Holm equations. Their related nonlinear short-wave model limits are then derived. A relation between the short-wave limit of the integrable Camassa-Holm equation and the Harry-Dym hierarchy is finally unveiled.