Wave Turbulence Under Parametric Excitation

Addressing the distinction between fully developed wave turbulence and parametric turbulence, this monograph describes various research projects currently taking place. Emphasis is placed on Hamiltonian formalism, multi-wave processes, modulation instabilities, wave collapses, S-theory and more.

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Wave turbulence is a state far from (thermodynamic) equilibrium. It can be observed in a stormy sea, a hot plasma, a dielectric in a powerful laser beam, in magnets exposed to strong microwave fields, etc. A distinction has to be made between fully developed turbulence and parametric turbulence. The latter is the subject of the present book. Addressing not only the expert but also the graduate student it gives a comprehensive review covering developments both in the West and in Eastern Europe where major research into this field has been done. Special attention is paid to the Hamiltonian formalism, multi-wave processes, modulation instabilities, self-focusing, wave collapses, S-theory, the mean-field approximation, chaos, Feynman diagrams, and comparison with experiments (magnons, spin waves).