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This book gives an overview of the theoretical research on rogue waves and discusses solutions to rogue wave formation via the Darboux and bilinear transformations, algebro-geometric reduction, and inverse scattering and similarity transformations. Studies on nonlinear optics are included, making the book a comprehensive reference for researchers in applied mathematics, optical physics, geophysics, and ocean engineering. ContentsThe Research Process for Rogue WavesConstruction of Rogue Wave Solution by the Generalized Darboux TransformationConstruction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering MethodThe Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model
Rogue waves. --- Rogue waves --- Extreme ocean waves --- Extreme storm waves --- Extreme waves --- Freak waves --- Giant waves --- Ocean waves --- Mathematical models. --- Darboux transformation. --- algebro-geometric reduction. --- bilinear transformation. --- nonlinear optics.
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Extreme, freak or rogue waves are produced by a number of physical mechanisms that focus the water-wave energy into a small area, due to wave instability, chaotic behaviour, dispersion (frequency modulation), refraction (presence of variable currents or bottom topography), soliton interactions, etc. During the past thirty years a number of physical models of the rogue wave phenomenon have been intensively developed. Numerous experimental, statistical and theoretical investigations are intended to understand the physics of the huge wave formation, its relation to the environmental conditions and to provide a freak wave design for engineering purposes. The book details the vast progress that has been achieved in the understanding of the physical mechanisms of rogue wave phenomenon in recent years. The selected articles address such issues as the formation of freak waves due to modulation instability of nonlinear wave field, physical and statistical properties of rogue wave generation in deep water and in shallow water, various models of nonlinear water waves, special analysis of nonlinear resonances between water waves and the relation between observations and freak wave theories. The book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and for students learning these subjects.
Rogue waves --- Mathematical models. --- Extreme ocean waves --- Extreme storm waves --- Extreme waves --- Freak waves --- Giant waves --- Ocean waves --- Oceanography. --- Physical geography. --- Geophysics/Geodesy. --- Classical and Continuum Physics. --- Geography --- Oceanography, Physical --- Oceanology --- Physical oceanography --- Thalassography --- Earth sciences --- Marine sciences --- Ocean --- Geophysics. --- Continuum physics. --- Geological physics --- Terrestrial physics --- Physics --- Classical field theory --- Continuum physics --- Continuum mechanics
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This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.
Physics. --- Geophysics. --- Fluids. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Geophysics/Geodesy. --- Optics, Lasers, Photonics, Optical Devices. --- Fluid- and Aerodynamics. --- Geophysics and Environmental Physics. --- Geological physics --- Terrestrial physics --- Natural philosophy --- Philosophy, Natural --- Physical geography. --- Geography --- Rogue waves. --- Extreme ocean waves --- Extreme storm waves --- Extreme waves --- Freak waves --- Giant waves --- Ocean waves --- Statistical physics. --- Lasers. --- Photonics. --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- New optics --- Optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Earth sciences --- Mathematical statistics --- Statistical methods
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This revised and updated second edition details the vast progress that has been achieved in the understanding of the physical mechanisms of rogue wave phenomenon in recent years. The selected articles address such issues as the formation of rogue waves due to modulational instability of nonlinear wave field, physical and statistical properties of extreme ocean wave generation in deep water as well as in shallow water, various models of nonlinear water waves, special analysis of nonlinear resonances between water waves and the relation between in situ observations, experimental data and rogue wave theories. In addition, recent results on tsunami waves due to subaerial landslides are presented.This book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and for students learning these subjects. Throughout the book, in fact, the reader will find a combination of theoretical and statistical/empirical treatment necessary for the complete examination of this subject. … Overall, ‘Extreme Ocean Waves’ is a valuable contribution to the literature on wave theory and statistics, helping fill an important gap in our knowledge of a variety of unusual waves. It should be of great interest to scientists and engineers studying physical oceanography, wave dynamics and observations, nonlinear physics, and applied mathematics.” (Eric L. Geist, Pure and Applied Geophysics, Vol. 168, 2011).
Marine Science --- Earth & Environmental Sciences --- Ocean waves. --- Rogue waves. --- Tsunamis. --- Storm surges. --- Hurricane waves --- Storm floods --- Storm tides --- Storm waves --- Surges, Storm --- Wind tides --- Earthquake sea waves --- Seismic sea waves --- Seismic surges --- Tidal waves --- Tunamis --- Extreme ocean waves --- Extreme storm waves --- Extreme waves --- Freak waves --- Giant waves --- Breakers --- Sea waves --- Surf --- Swell --- Natural disasters --- Ocean waves --- Oceanography --- Water waves --- Floods --- Oceanography. --- Physical geography. --- Geology. --- Geophysics/Geodesy. --- Natural Hazards. --- Geophysics and Environmental Physics. --- Geognosy --- Geoscience --- Earth sciences --- Natural history --- Geography --- Oceanography, Physical --- Oceanology --- Physical oceanography --- Thalassography --- Marine sciences --- Ocean --- Geophysics. --- Natural disasters. --- Natural calamities --- Disasters --- Geological physics --- Terrestrial physics --- Physics
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