Research article

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

  • Received: 20 October 2017 Accepted: 31 October 2017 Published: 06 November 2017
  • 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.

    Citation: 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

    Related Papers:

  • 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.


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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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