FULL SYMMETRY ALGEBRA FOR ODE'S AND CONTROL SYSTEMS
Author: Alexey SAMOKHIN
A description of the full symmetry algebra (i.e., including higher
symmetries) for a general nonlinear system of ordinary differential
equations is given in terms of its general solution and
differential constants. More precisely, the full symmetry algebra of a
system is a module over the ring of its
differential constants; the module is generated by partial derivatives of
the general solution by the independent constants.
Given a general solution, this description
is both effective and explicit. Special solutions, such as
an envelope of a family
of solutions is described naturally in this context.
These results are extended to
control systems; in this case
the differential constants become operators on controls.
Examples are provided.
13 pages, LaTeX-2e (AmSLaTeX 1.2) and EPSF.STY.
To compile source files (.tex) one needs the title page style files titlatex.tex.