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Regular version of the site

Article

Probabilistic characteristics of nonlinear waves in nondispersive media of the hydrodynamic type

Gurbatov S., Pelinovsky E.

The paper considers the probability distributions of the nonlinear wave characteristics in nondispersive media
that satisfy the Riemann- and the Kardar-Parisi-Zhang-type equations. By using the Lagrangian and Euler
relations of statistical descriptions, expressions are obtained for the probability density of the Riemann wave
(displacement) integral through the initial probability density of displacement, velocity, and acceleration. The
case of Gaussian initial statistics is considered when multivalued sections in nonlinear waves arise at arbitrarily
small distances from the entrance. The expressions obtained in this case should be interpreted as the relative
residence time of the process in a certain displacement range. It is shown that, due to the Riemann equation
locality, the appearance of ambiguity in the wave profile, which occurs mainly at negative values, does not affect
the probability density form at positive bias values.