Differential and Integral Equations

KdV invariants and Herglotz functions

Alexei Rybkin

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A new approach to deriving trace-type formulas is given. In this way, a new representation for the densities of the first integrals of the Korteweg-de Vries equation are found in terms of spectral and scattering data of the associated Schrödinger operator. We also utilize our method to improve many already-known results on the KdV invariants and associated trace formulas.

Article information

Differential Integral Equations, Volume 14, Number 4 (2001), 493-512.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.)
Secondary: 35C05: Solutions in closed form 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]


Rybkin, Alexei. KdV invariants and Herglotz functions. Differential Integral Equations 14 (2001), no. 4, 493--512. https://projecteuclid.org/euclid.die/1356123317

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