# Properties of solutions to linear KdV equations with φ-sub-Gaussian initial conditions

## DOI:

https://doi.org/10.17721/1812-5409.2022/2.1## Keywords:

φ-sub-Gaussian processes, Airy equation, random initial condition, distribution of supremum## Abstract

In this paper, there are studied sample paths properties of stochastic processes representing solutions (in L_2(Ω) sense) to the linear Korteweg–de Vries equation (called also the Airy equation) with random initial conditions given by φ-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded domains. Also, there are presented some examples to illustrate the results of the study.

* Pages of the article in the issue*: 11 - 19

** Language of the article**: English

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*Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics*, (2), 11–19. https://doi.org/10.17721/1812-5409.2022/2.1

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