Lie-point symmetries and nonlinear dynamical systems
نویسندگان
چکیده
منابع مشابه
Lie Point Symmetries for Reduced Ermakov Systems
Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2, R) always is a group of point symmetries for the reduced Ermakov systems. The theory is applied to a model example and to the equations of ...
متن کاملLie-point Symmetries and Nonlinear Dynamical Systems (symmetry and Approximate Symmetries of Nonlinear Equations: Bifurcations, Center Manifolds, and Normal Form Reduction)
Nonlinear symmetries of nite dimensional dynamical systems are related to nonlinear normal forms and center manifolds in the neighbourhood of a singular point. Certain abstract results can be used algorith-mically to construct the normal forms and/or the center manifold up to a given order in the perturbation expansion. We also argue that for this task, approximate symmetries are as useful as e...
متن کاملNonlinear Diffusion-Convection Systems: Lie and Q-Conditional Symmetries
arising in several application [4]. Lie symmetry of BEq was found in [5], while the Q-conditional symmetry (i.e., non-classical symmetry [6]) was described in [7] and [8]. In the general case a wide list of Lie symmetries for DC equations of the form (1) is presented in [9]. A complete description of Lie symmetries, i.e., group classification of (1) has been done in [10]. The Q-conditional symm...
متن کاملC∞−Symmetries and Reduction of Equations Without Lie Point Symmetries
It is proved that several usual methods of reduction for ordinary differential equations, that do not come from the Lie theory, are derived from the existence of C∞ -symmetries. This kind of symmetries is also applied to obtain two successive reductions of an equation that lacks Lie point symmetries but is a reduced equation of another one with a three dimensional Lie algebra of point symmetrie...
متن کاملPolynomial and non-polynomial solutions set for wave equation with using Lie point symmetries
This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE). We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry. We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation. A generalized procedure for polynomial solution is pr...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 1997
ISSN: 0895-7177
DOI: 10.1016/s0895-7177(97)00062-9