Lie point symmetries and reductions of one-dimensional equations describing perfect Korteweg-type nematic fluids
| Autor: | Luigi Martina, Giovanni De Matteis |
|---|---|
| Přispěvatelé: | G., De Mattei, Martina, Luigi |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Dynamical systems theory
Differential equation Independent equation Mathematical analysis Nonlinear dynamic Lie group Statistical and Nonlinear Physics Partial differential equation Euler equations Liquid Crystals symbols.namesake Simultaneous equations symbols Differential algebraic equation Lie algebras of Lie group Mathematical Physics Mathematics Numerical partial differential equations Mathematical physics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|