Linear and Nonlinear Wave Processes: an Elementary Introduction to the Theory of Hamiltonian Variables with Physical and Astrophysical Applications

摘要

Using the examples of bulk and surface waves in the liquid, procedures for the introduction of the Hamiltonian variables for continuous media are discussed, which are widely used in plasma physics, hydrodynamics and field theory. Regular ways of introducing such variables, including the case of media with discontinuities, are considered, based on the variational principle and canonical transformations. The inverse scattering problem is presented as a nontrivial case of canonical transformation to the "action-angle" variables. Examples of linear and nonlinear instabilities are given. The present paper is Part Ⅰ of a review whose Part Ⅱ will be devoted to the kinetic equations of weak turbulence, including exact methods of deriving nonequilibrium flux controlled distributions. Examples are given of applying the Smoluchowski kinetic equation to the analysis of merging galaxies and formation of their mass spectra. Also, nonlocal distributions and partially coherent systems are considered.