Premium
Geometric Aspects of Spatially Periodic Interfacial Waves
Author(s) -
Dias Frédéric,
Bridges Thomas J.
Publication year - 1994
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm199493293
Subject(s) - hamiltonian system , classical mechanics , standing wave , nonlinear system , hamiltonian (control theory) , physics , mathematical analysis , inviscid flow , singularity , bifurcation , mathematics , invariant (physics) , mathematical physics , optics , quantum mechanics , mathematical optimization
Periodic waves at the interface between two inviscid fluids of differing densities are considered from a geometric point of view. A new Hamiltonian formulation is used in the analysis and restriction of the Hamiltonian structure to space‐periodic functions leads to an O ‐invariant Hamiltonian system. Motivated by the simplest O ‐invariant Hamiltonian system, the spherical pendulum, we analyze the properties of traveling waves, standing waves, interactions between standing and traveling waves (mixed waves) and time‐modulated spatially periodic waves. A singularity in the bifurcation of traveling waves leads to a nonlinear resonance and this is investigated numerically.