AIMS Mathematics, 2017, 2(4): 610-621. doi: 10.3934/Math.2017.4.610.

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

Department of Mathematics, University of Texas, TX 78539-2999 Edinburg, USA

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.
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Keywords integrable; prolongation; connection; differential system; bundle; conservation law; Frobenius

Citation: Paul Bracken. A geometric formulation of Lax integrability for nonlinear equationsin two independent variables. AIMS Mathematics, 2017, 2(4): 610-621. doi: 10.3934/Math.2017.4.610

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