Asymptotics of Long Nonlinear Propagating Waves in a One-Dimensional Basin with Gentle Shoresстатья
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Дата последнего поиска статьи во внешних источниках: 26 января 2024 г.
Аннотация:The Cauchy problem for a one-dimensional (nonlinear) shallow water equations over a variable bottom D(x) is considered in an extended basin bounded from two sides by shores (where the bottom degenerates, D(a) = 0), or by a shore and a wall. The short-wave asymptotics of the linearized system in the form of a propagating localized wave is constructed. After applying to the constructed functions a simple parametric or explicit change of variables proposed in recent papers (Dobrokhotov, Minenkov, Nazaikinsky, 2022 andDobrokhotov, Kalinichenko, Minenkov, Nazaikinsky, 2023), we obtain the asymptotics of the original nonlinear problem. On the constructed families of functions, the ratio of the amplitude and the wavelength is studied for which hte wave does not collapse when running up to the shore.The work was carried out within the framework of the Russian Science Foundation grant 21-11-00341.