A geometric formulation of Lax integrability is introduced which makes use of a Pfaffan formulation of Lax integrability. The Frobenius theorem gives a necessary and suffcient condition for the complete integrability of a distribution, and provides a powerful way to study nonlinear evolution equations. This permits an examination of the relation between complete integrability and Lax integrability. The prolongation method is formulated in this context and gauge transformations can be examined in terms of differential forms as well as the Frobenius theorem.
Paul Bracken. A geometric formulation of Lax integrability for nonlinear equationsin two independent variables[J]. AIMS Mathematics, 2017, 2(4): 610-621. doi: 10.3934/Math.2017.4.610
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