Jones, Mark and Hunter, Gordon (2019) Conservation laws for a non-linear system describing the propagation of "triadic" waves. Proceedings of the Institute of Acoustics, 41(1), pp. 137-145. ISSN (print) 1478-6095
Abstract
When two waves, be they sound waves, waves in a liquid or electromagnetic waves, of different wavenumbers travel at the same speed, they may interact nonlinearly and resonance can arise. In this paper we shall be especially concerned with capillary-gravity waves (that is, waves which are subject to the twin restoring forces of gravity and surface tension) on the surface of deep water. However, our theory could just as well be applied to any physical wave system where the evolution of the waves is governed by an asymptotic balance between the effects of nonlinearity and dispersion. One obvious generalization is to interfacial waves between two fluids, but other examples are light pulses propagating along an optical fibre, waves in a hot electron plasma, or ‘beat’ waves. In this report we shall be studying the case of ‘one-three’ (i.e. ‘triadic’) resonance when the interaction occurs between the fundamental mode and its third harmonic (i.e. a wave with a third of the wavelength of the fundamental).
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