Hugoniót--Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations

被引：0

作者：

E. S. Semenov

机构：

[1] Russian Scientific Center “Kurchatov Institute”,Institute of Natural Science and Ecology

来源：

Mathematical Notes | 2002年 / 71卷

关键词：

quasilinear hyperbolic equations; vortex type singularity; Hugoniót--Maslov condition; shallow water equations;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

For the “phase” of vortex singular solutions of the shallow water equations we justify the Hamilton--Jacobi equation corresponding to the hydrodynamical mode of perturbation propagation. We also obtain the next correction to the Cauchy--Riemann conditions describing how the singular part of the solution affects the smooth background.

引用

页码：825 / 835

页数：10

共 8 条

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[2] Maslov V. P.(1980)Three algebras corresponding to nonsmooth solutions of systems of quasilinear hyperbolic equations Uspekhi Mat. Nauk [Russian Math. Surveys] 35 252-253
[3] Dobrokhotov S. Y.(2001)Proof of Maslov's conjecture about the structure of weak-point singular solutions of the shallow water equations Russian J. Math. Phys. 8 25-54
[4] Pankrashkin K. V.(1999)Hugoniót-Maslov chains for solitary vortices of the shallow water equations. I Russian J. Math. Phys. 6 137-173
[5] Semenov E. S.(1999)Hugoniót-Maslov chains for solitary vortices of the shallow water equations. II Russian J. Math. Phys. 6 282-313
[6] Dobrokhotov S. Y.(2000)Integrability effects in truncatedHu goniót-Maslov chains for trajectories of mesoscale vortices on shallow water Teoret. Mat. Fiz. [Theoret. and Math. Phys.] 125 491-518
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