Maurer–cartan Equations for Lie Symmetry Pseudo-groups of Differential Equations
نویسندگان
چکیده
A new method of constructing structure equations of Lie symmetry pseudo-groups of differential equations, dispensing with explicit solutions of the (infinitesimal) determining systems of the pseudo-groups, is presented, and illustrated by the examples of the Kadomtsev–Petviashvili and Korteweg–de-Vries equations.
منابع مشابه
Pseudo–groups, Moving Frames, and Differential Invariants
We survey recent developments in the method of moving frames for infinite-dimensional Lie pseudo-groups. These include a new, direct approach to the construction of invariant Maurer–Cartan forms and the Cartan structure equations for pseudo-groups, and new algorithms, based on constructive commutative algebra, for establishing the structure of their differential invariant algebras.
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This paper begins a series devoted to developing a general and practical theory of moving frames for infinite-dimensional Lie pseudo-groups. In this first, preparatory part, we present a new, direct approach to the construction of invariant Maurer–Cartan forms and the Cartan structure equations for a pseudo-group. Our approach is completely explicit and avoids reliance on the theory of exterior...
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We survey a recent extension of the moving frames method for infinite-dimensional Lie pseudo-groups. Applications include a new, direct approach to the construction of Maurer–Cartan forms and their structure equations for pseudogroups, and new algorithms, based on constructive commutative algebra, for uncovering the structure of the algebra of differential invariants for pseudogroup actions.
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متن کاملMoving Frames for Pseudo–Groups. I. The Maurer–Cartan Forms
This paper begins a series devoted to developing general and practical theory of moving frames for infinite-dimensional Lie pseudo-groups. In this first, preparatory part, we present a new, direct approach to the construction of invariant Maurer–Cartan forms and the Cartan structure equations for a pseudo-group. Our approach is completely explicit and avoids reliance on the theory of exterior d...
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تاریخ انتشار 2005