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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Conservation laws for a class of third order evolutionary differential systems
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by Sung Ho Wang PDF
Trans. Amer. Math. Soc. 356 (2004), 4055-4073 Request permission

Abstract:

Conservation laws of third order quasi-linear scalar evolution equations are studied via exterior differential system and characteristic cohomology. We find a subspace of 2-forms in the infinite prolongation space in which every conservation law has a unique representative. Analysis of the structure of this subspace based upon the symbol of the differential equation leads to a universal integrability condition for an evolution equation to admit any higher order (weight) conservation laws. As an example, we give a complete classification of a class of evolution equations which admit conservation laws of the first three consecutive weights $-1$, $1$, $3$. The differential system describing the flow of a curve in the plane by the derivative of its curvature with respect to the arc length is also shown to exhibit the KdV property, i.e., an infinite sequence of conservation laws of distinct weights.
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Additional Information
  • Sung Ho Wang
  • Affiliation: Department of Mathematics, Postech, Pohang, Korea 790-784
  • Email: wang@postech.ac.kr
  • Received by editor(s): June 9, 2003
  • Received by editor(s) in revised form: July 8, 2003
  • Published electronically: February 27, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 4055-4073
  • MSC (2000): Primary 35K25; Secondary 58A15
  • DOI: https://doi.org/10.1090/S0002-9947-04-03501-9
  • MathSciNet review: 2058518