Group classification of the two-dimensional shallow water equations with the beta-plane approximation of coriolis parameter in Lagrangian coordinates

摘要

Two-dimensional shallow water equations with uneven bottom and a Coriolis parameter f = f(0) + beta y, (beta not equal 0) in mass Lagrangian coordinates are studied in this paper. The equa-tions describing these flows are reduced to two Euler-Lagrange equations. The paper pro-vides a complete group classification of the equations and applications of Noether's theo-rem for constructing conservation laws. (C) 2020 Elsevier B.V. All rights reserved.