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Nonlinear Water Waves
Wave motion in water is one of the most striking observable phenomena in nature. Throughout the twentieth century, development of the linearized theory of wave motion in fluids and hydrodynamic stability has been steady and significant. In the last three decades there have been remarkable developments in nonlinear dispersive waves in general, nonlinear water waves in particular, and nonlinear instability phenomena. New solutions are now available for waves modulatedin both space and time, which exhibit new phenomena as diverse as solitons, resonant interactions, side-band instability, and wave-breaking. Other achievements include the discovery of soliton interactions, and the Inverse Scattering Transform method forfinding the explicit exact solution for several canonical nonlinear partial differential equations.
This monograph is the first to summarize the research on nonlinear wave phenomena over the past three decades, and it also presents numerous applications in physics, geophysics, and engineering.
Basic Equations of Motion of Inviscid and Viscous Fluids. The Theory of Surface Waves on Water. Transient Wave Motions in an Inviscid Fluid. Nonlinear Shallow Water Waves and Solitons. Ship Waves and Wave Resistance. NonlinearDiffraction of Water Waves. The Theory of Nonlinear Dispersive Waves. Nonlinear Instability of Dispersive Waves with Applications to Water Waves. Bibliography. Index.