Symmetries of the shallow water equations in the Boussinesq approximation

•Symmetries of the shallow water equations in the Boussinesq approximation are studied.•Two different Lagrangians are considered.•Conservations laws of the equations studied were found by using Noether’s theorem. The shallow water equations in the Boussinesq approximation are studied in this paper....

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2019-02, Vol.67, p.1-12
Main Authors: Voraka, Prakrong, Kaewmanee, Chompit, Meleshko, Sergey V.
Format: Article
Language:English
Subjects:
Approximation
Boussinesq approximation
Conservation laws
Invariant solution
Lie group
Lie groups
Mathematical analysis
Noether’s theorem
Shallow water equations
Symmetry
Water
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Summary:•Symmetries of the shallow water equations in the Boussinesq approximation are studied.•Two different Lagrangians are considered.•Conservations laws of the equations studied were found by using Noether’s theorem. The shallow water equations in the Boussinesq approximation are studied in this paper. Two cases of these equations are studied: in Eulerian coordinates and Lagrangian coordinates. A detailed analysis of the admitted Lie groups is given. All invariant solutions of these two representations are presented. Using Noether’s theorem, new conservation laws in Eulerian coordinate and Lagrangian coordinates are found.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2018.06.028