Nonlinear Deep Water Waves: A Physical Testing Ground for Solitons and Recurrence
The physical problem that we are concerned with is the evolution of nonlinear deep water waves. We shall assume that the waves under consideration are long enough so that the effect of surface tension is small compared to gravity (hence, they are sometimes referred to as “gravity waves”). This requires that the waves be much longer than 10 cm, at which wavelength surface tension and gravitational effects are comparable to each other. We shall assume that the water motion is incompressible, irrotational and inviscid. These are the usual approximations that go with the study of water waves, and are expected to be satisfied under normal circumstances. We shall also assume that the depth of the water is much larger than a typical wavelength. This deep water assumption is the opposite of the shallow water limit which leads to the well known Korteweg-de Vries equation-the first equation found to exhibit permanent, localized waveform solutions now known as solitons.
KeywordsWave Pulse Water Wave Fluid Mechanics Nonlinear Evolution Equation Envelope Soliton
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