Conservation laws and symmetries of the shallow water system above rough bottom

All-Russian conference on Nonlinear Waves: Theory and New Applications

Aksenov, A.V.^1 ; Druzhkov, K.P.^1

Lomonosov Moscow State University, Moscow, Russia^1

关键词: Change of variables;    Conservation law;    Group classification;    One-dimensional shallow water equations;    Shallow water equations;    Shallow-water systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012001/pdf
DOI  :  10.1088/1742-6596/722/1/012001

来源: IOP

【 摘 要 】

The system of one-dimensional shallow water equations above the rough bottom is considered. All its hydrodynamic conservation laws are found, and a group classification is performed. A new conservation law additional to the two basic conservation laws is found. It is shown that the system of shallow water equations can be linearized by a point change of variables only in cases of constant and linear bottom profiles.