Nonlinear Waves and Weak Turbulence

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Brand new. We distribute directly for the publisher. This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive ... conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincar?? normal forms, and the inverse scattering method. Read more Show Less

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Overview

This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincare normal forms, and the inverse scattering method.

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Editorial Reviews

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Six papers devoted to different aspects of the theory of nonlinear waves propagating in dispersive conservative media, which has developed over the past three decades to become an established part of mathematical physics. They emphasize weakly interacting waves on the surface of an ideal fluid, and Rossby waves in the atmosphere, and show how the theory is naturally related to such areas of mathematics as Diophantine equations, the differential geometry of waves, Poincar<'e> normal forms, and the inverse scattering method. Member prices are $71 for institutions and $53 for individuals. No index. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Introduction
Invariants of Wave Systems and Web Geometry 1
Stability of Weak-Turbulence Kolmogorov Spectra 31
Energy Transfer in the Spectrum of Surface Gravity Waves by Resonance Five Wave-Wave Interactions 83
Wave Resonances in Systems with Discrete Spectra 95
Hamiltonian Formalism for Rossby Waves 131
Weakly Nonlinear Waves on the Surface of an Ideal Finite Depth Fluid 167
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