Conservation laws of the equation of one-dimensional shallow water over uneven bottom in Lagrange’s variables

2020 ◽  
Vol 119 ◽  
pp. 103348 ◽  
Author(s):  
Alexander V. Aksenov ◽  
Konstantin P. Druzhkov
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
One Dimensional ◽  
Uneven Bottom

CONSERVATION LAWS FOR ONE-DIMENSIONAL SHALLOW WATER MODELS FOR ONE AND TWO-LAYER FLOWS

2006 ◽  
Vol 16 (01) ◽  
pp. 119-137 ◽  
Author(s):  
RICARDO BARROS
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Shallow Water Model ◽  
Frobenius Problem ◽  
One Dimensional ◽  
Shallow Water Models ◽  
The One ◽  
Open Question

A full set of conservation laws for the two-layer shallow water equations is presented for the one-dimensional case. We prove that all the conservation laws are linear combination of the equations for the conservation of mass and velocity (in each layer), total momentum and total energy.This result generalizes that of Montgomery and Moodie that found the same conserved quantities by restricting their search to the multinomials expressions in the layer variables. Though the question of whether or not there are only a finite number of these quantities is left as an open question by the authors. Our work puts an end to this: in fact, no more conservation laws are admitted for the two-layer shallow water equations. The key mathematical ingredient of the method proposed leading to the result is the Frobenius problem. Moreover, we present a full set of conservation laws for the classical one-dimensional shallow water model with topography, by using the same techniques.

scholarly journals Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 364-370 ◽  
Author(s):  
Dumitru Baleanu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Aliyu Isa Aliyu
Keyword(s):  
Exact Solution ◽  
Wave Equation ◽  
Conservation Laws ◽  
Shallow Water ◽  
Water Wave ◽  
Airy Function ◽  
One Dimensional ◽  
Shallow Water Wave ◽  
Differential Substitution ◽  
Conservation Theorem

AbstractIn this article, the generalized shallow water wave (GSWW) equation is studied from the perspective of one dimensional optimal systems and their conservation laws (Cls). Some reduction and a new exact solution are obtained from known solutions to one dimensional optimal systems. Some of the solutions obtained involve expressions with Bessel function and Airy function [1,2,3]. The GSWW is a nonlinear self-adjoint (NSA) with the suitable differential substitution, Cls are constructed using the new conservation theorem.

Conservation Laws on Surfaces: Meteorological Systems—Shallow-Water

2011 ◽  
Author(s):  
Matania Ben-Artzi ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Meteorological Systems

scholarly journals Conservation laws and integrability of a one-dimensional model of diffusing dimers

1997 ◽  
Vol 86 (5-6) ◽  
pp. 1237-1263 ◽  
Author(s):  
Gautam I. Menon ◽  
Mustansir Barma ◽  
Deepak Dhar
Keyword(s):  
Conservation Laws ◽  
Dimensional Model ◽  
One Dimensional
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