Table of Contents

Part 1 One-dimensional waves in nonlinear nondispersive media: the basic equations and statistical problems of the theory of random waves in nondispersive media; physical examples of nonlinear waves. Part 2 One-dimensional wave dynamics: exact solution of Burgers equation, Reynolds number; Burgers equation solution at large Reynolds numbers; evolution of the basic disturbance types; Burghers equation, hydrodynamics of noninteracting particles and parabolic equation quasioptics. Part 3 Lagrangian and Eulerian statistics of random fields: connection of the statistical properties of random fields; connection of statistical properties of random functions with behaviour of their realizations; Lagrangian and Eulerian statistics of random fields. Part 4 Random waves of hydrodynamic type: probability properties of random Riemann waves; Riemann wave spectrum; density fluctuations of noninteracting particle gas; probability properties of density fluctuations; fluctuations of the optical wave parameters beyond a random phase screen; concentrations of a passive impurity in a flow with random velocity field; motion of noninteracting particles under the action of external forces. Part 5 Statistical properties of discontinuous waves: discontinuity influence on the nonlinear wave statistics - initial stage; qualitative theory of one-dimensional turbulence at the stage of developed discontinuities; self-preservation of random waves in nonlinear dissipative media; asymptotic analysis of nonlinear random waves at large Reynolds numbers; turbulence at finite Reynolds numbers - final stage of decay; statistical properties of the waves in a medium with arbitrary nonlinearity. Part 6 Three-dimensional potential turbulence - the large-scale structure of the Universe: cellular structure formation in three-dimensional potential turbulence; asymptotic features of potantial turbulence; density fluctuations in model gas. Appendices: Properties of delta-functions and their statistical averages; nonlinear gravitational instability of random density waves in the expanding universe, A.L.Melott and S.F.Shandarin; singularities and bifurcations of potential flows, V.I.Arnold et al.