By
Alfred Osborne, University of Torino, Italy
Description
For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics
of linear wave trains.
Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear
Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water
waves, internal waves, and equatorial Rossby waves. This revolutionary development will allow hyperfast numerical modelling of nonlinear
waves, greatly advancing our understanding of oceanic surface and internal waves. Nonlinear Fourier analysis is based upon a generalization
of linear Fourier analysis referred to as the
inverse scattering transform, the fundamental building block of which is
a generalized Fourier series called the Riemann theta function. Elucidating the art and science of implementing these functions in the
context of physical and time series analysis is the goal of this book.
Included in series
International Geophysics
Audience:
Academia, government, and industry in the fields of ocean sciences, geophysics, and engineering mathematics.
