A geometric formulation of Lax integrability for nonlinear equationsin two independent variables

Abstract

A geometric formulation of Lax integrability is introduced which makes use of a Pfaffianformulation of Lax integrability. The Frobenius theorem gives a necessary and sufficient conditionfor the complete integrability of a distribution, andprovides a powerful way to study nonlinear evolution equations. This permits an examination of the relationbetween complete integrability and Lax integrability. The prolongation method is formulated in this contextand gauge transformations can be examined in terms ofdifferential forms as well as the Frobenius theorem.

Keywords

• integrable| prolongation| connection| differential system| bundle| conservation law| Frobenius