Conservation laws of the system of equations of one-dimensional shallow water over uneven bottom in Lagrange's variables

2018/12/12 by А. В. Аксенов, Aksenov, Alexander V., Konstantin P. Druzhkov +1
Earth and Planetary Sciences · #Coastal and Marine Dynamics #Aquatic and Environmental Studies #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.1812.05096

Abstract

The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of equations is used to find all first order conservation laws of shallow water equations in Lagrange's variable for all bottom profiles. The obtained conservation laws are compared with the hydrodynamic conservation laws of the system of equations of one-dimensional shallow water over uneven bottom in Euler's variables. Bottom profiles are given for which there are additional conservation laws.

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