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.

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