2020 journal article

The one-dimensional Green-Naghdi equations with a time dependent bottom topography and their conservation laws


By: E. Kaptsov, S. Meleshko n & N. Samatova n

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: January 11, 2021

This paper deals with the one-dimensional Green–Naghdi equations describing the behavior of fluid flow over an uneven bottom topography depending on time. Using Matsuno’s approach, the corresponding equations are derived in Eulerian coordinates. Further study is performed in Lagrangian coordinates. This study allowed us to find the general form of the Lagrangian corresponding to the analyzed equations. Then, Noether’s theorem is used to derive conservation laws. As some of the tools in the application of Noether’s theorem are admitted generators, a complete group classification of the Green–Naghdi equations with respect to the bottom depending on time is performed. Using Noether’s theorem, the found Lagrangians, and the group classification, conservation laws of the one-dimensional Green–Naghdi equations with uneven bottom topography depending on time are obtained.