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pro vyhledávání: '"Mansfield, Elizabeth L."'
Autor:
Mansfield, Elizabeth L.
We outline how discrete analogues of the conservation of potential vorticity may be achieved in Finite Element numerical schemes for a variational system which has the particle relabelling symmetry, typically shallow water equations. We show that the
Externí odkaz:
http://arxiv.org/abs/2304.10913
Publikováno v:
Forum Math. Sigma (2016), Vol. 4, e29, 55 pages
In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how to obtain
Externí odkaz:
http://arxiv.org/abs/1306.0847
Publikováno v:
Studies in Applied Mathematics 130: 134-166, 2012
Noether's First Theorem yields conservation laws for Lagrangians with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. In re
Externí odkaz:
http://arxiv.org/abs/1106.3964
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational problem whos
Externí odkaz:
http://arxiv.org/abs/1103.3267
Publikováno v:
Studies in Applied Mathematics 128: 1-29 2011
Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. The aim of
Externí odkaz:
http://arxiv.org/abs/1006.4660
In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation $$u_{xxxt} + \alpha u_x u_{xt} + \beta u_t u_{xx} - u_{xt} - u_{xx} = 0,\eqno(1)$$ where $\alpha$ and $\beta$ are arbitrary, nonzero, constants, w
Externí odkaz:
http://arxiv.org/abs/solv-int/9409003
In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et. al. [Stud. Appl. Math., 53 (1974) 249--315] and one by Hirota and Satsuma [J. Ph
Externí odkaz:
http://arxiv.org/abs/solv-int/9401003
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This algorithm requ
Externí odkaz:
http://arxiv.org/abs/solv-int/9401002
Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gr\"obner bases is used both to find the conditions on $f(u)$ under which symmetries other than the trivial s
Externí odkaz:
http://arxiv.org/abs/solv-int/9306002
Publikováno v:
Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 1996 Jul . 354(1713), 1807-1835.
Externí odkaz:
https://www.jstor.org/stable/54627
