Asymptotic localized solutions of the shallow water equations over a nonuniform bottom

Dobrokhotov, S. Yu.; Назайкинский, В. Е.

doi:10.1063/1.5082098

AIP Conference Proceedings

2018

DOI: 10.1063/1.5082098

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Asymptotic localized solutions of the shallow water equations over a nonuniform bottom

S. Yu. Dobrokhotov¹,

В. Е. Назайкинский²

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Cited by 3 publications

References 66 publications

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Nonstandard caustics for localized solutions of the 2d shallow water equations with applications to wave propagation and run-up on a shallow beach

Dobrokhotov

Назайкинский

2020

J. Phys.: Conf. Ser.

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The usual semiclassical approximation is not directly applicable to linearized two-dimensional shallow water equations with localized initial data describing long waves (for example, tsunami waves) in a bounded basin of variable depth, because the momentum variables on the geometric optics rays become infinite at the boundary of the region. To obtain asymptotic solutions, one needs to extend the phase space and introduce a modified Maslov canonical operator. The paper gives a brief survey of some results obtained in this direction by the authors and their colleagues.

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Nonstandard caustics for localized solutions of the 2d shallow water equations with applications to wave propagation and run-up on a shallow beach

Dobrokhotov

Назайкинский

2020

J. Phys.: Conf. Ser.

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Efficient Asymptotics in Problems on the Propagation of Waves Generated by Localized Sources in Linear Multidimensional Inhomogeneous and Dispersive Media

Dobrokhotov

Назайкинский

2020

Comput. Math. and Math. Phys.

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Modeling of 2D Acoustic Radiation Patterns as a Control Problem

et al. 2022

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A problem of modeling radiation patterns of wave sources in two-dimensional acoustic tomography is considered. Each source has its own radiation patterns, and their modeling will be used to improve the solvability of inverse problems of recovering the acoustic parameters of human soft tissues and come closer to building a digital twin of acoustic tomography. The problem is considered as a control problem of the right side for the velocities by spatial variables. Two statements are investigated—control by time or space functions. A numerical solution method is implemented. The results of numerical calculations are presented.

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Asymptotic localized solutions of the shallow water equations over a nonuniform bottom

Cited by 3 publications

References 66 publications

Nonstandard caustics for localized solutions of the 2d shallow water equations with applications to wave propagation and run-up on a shallow beach

Nonstandard caustics for localized solutions of the 2d shallow water equations with applications to wave propagation and run-up on a shallow beach

Efficient Asymptotics in Problems on the Propagation of Waves Generated by Localized Sources in Linear Multidimensional Inhomogeneous and Dispersive Media

Modeling of 2D Acoustic Radiation Patterns as a Control Problem

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