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Topics in Operator Theory pp 427–444Cite as

Regularized Perturbation Determinants and KdV Conservation Laws for Irregular Initial Profiles

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 203))

Abstract

In the context of the Korteweg-de Vries equation we put forward some new conservation laws which hold for real initial profiles with low regularity. Some applications to spectral theory of the one-dimensional Schrödinger operator with singular potentials are also considered.

Based on research supported in part by the US National Science Foundation under Grant DMS 070747.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematical and Statistics, University of Alaska Fairbanks, PO Box 756660, Fairbanks, AK, 99775, USA

    Alexei Rybkin

Authors
  1. Alexei Rybkin
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. Department of Mathematics, College of William and Mary, P. O. Box 8795, Williamsburg, VA, 23187-8795, USA

    Vladimir Bolotnikov , Leiba Rodman  & Ilya M. Spitkovsky ,  & 

  3. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112

    J. William Helton

Additional information

Dedicated to Israel Gohberg on the occasion of his 80th birthday. We first learned about regularized determinants from one of his books with Mark Krein.

Communicated by I.M. Spitkovsky.

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© 2010 Birkhäuser Verlag Basel/Switzerland

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Rybkin, A. (2010). Regularized Perturbation Determinants and KdV Conservation Laws for Irregular Initial Profiles. In: Ball, J.A., Bolotnikov, V., Rodman, L., Spitkovsky, I.M., Helton, J.W. (eds) Topics in Operator Theory. Operator Theory: Advances and Applications, vol 203. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0161-0_17

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