Superposition formulas for exterior differential systems

Superposition Formulas for Exterior Differential Systems

Superposition Formulas for Darboux Integrable Exterior Differential Systems

1 Introduction 1 1 Introduction In this paper we present a far-reaching generalization of E. Vessiot's analysis [24], [25] of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical method, uncovers the fundamental geometric invariants of Dar-boux integrable systems, and provides for systematic,...

Exterior Differential Systems ∗

We will denote by 〈γ1, ..., γk〉 the differential ideal generated by γ1, ..., γk, i.e. the set of elements of Ω∗(M) of the form α ∧ γ1 + ...+ α ∧ γk + β ∧ dγ1 + ...+ β ∧ dγk, for some α, ..., α, β, ..., β ∈ Ω∗(M). We also denote by 〈γ1, ..., γk〉alg the “algebraic” ideal (not necessarily closed under d) consisting of elements of the form α ∧ γ1 + ...+ α ∧ γk. The basic problem of EDS is to find i...

Notes on Exterior Differential Systems

These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.

Solutions of Nonlinear Differential and Difference Equations with Superposition Formulas

Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit solutions of certain classes of scalar and matrix Riccati equations are presented as an illustration of the general results. Typeset using REVTEX 1