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, Poincaré normal forms, and the inverse scattering method.

Readership

Graduate students and research mathematicians interested in the theory of nonlinear waves and its applications.

Table of Contents

• A. M. Balk and E. V. Ferapontov -- Invariants of wave systems and web geometry
• A. M. Balk and V. E. Zakharov -- Stability of weak-turbulence Kolmogorov spectra
• V. A. Kalmykov -- Energy transfer in the spectrum of surface gravity waves by resonance five wave-wave interactions
• E. Kartashova -- Wave resonances in systems with discrete spectra
• L. I. Piterbarg -- Hamiltonian formalism for Rossby waves
• V. E. Zakharov -- Weakly nonlinear waves on the surface of an ideal finite depth fluid