Lie point symmetries and reductions of one-dimensional equations describing perfect Korteweg-type nematic fluids

De Matteis, Giovanni and Martina, Luigi (2012) Lie point symmetries and reductions of one-dimensional equations describing perfect Korteweg-type nematic fluids. Journal of Mathematical Physics, 53 (3). 033101. ISSN 0022-2488

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Abstract

A system of partial differential equations, describing one-dimensional nematic liquid crystals is studied by Lie group analysis. These equations are the Euler–Lagrange equations associated with a free energy functional that depends on the mass density and the gradient of the mass density. The group analysis is an algorithmic approach that allows us to show all the point symmetries of the system, to determine all possible symmetry reductions and, finally, to obtain invariant solutions in the form of travelling waves. The Hamiltonian formulation of the dynamical equations is also considered and the conservation laws found by exploiting the local symmetries.

Item Type:	Article
Subjects:	F300 Physics G100 Mathematics
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Ay Okpokam
Date Deposited:	09 Apr 2013 08:28
Last Modified:	13 Oct 2019 00:31
URI:	http://nrl.northumbria.ac.uk/id/eprint/12037

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