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Zbl 0697.35125
Tracy, E.R.; Larson, J.W.; Osborne, A.R.; Bergamasco, L.
On the nonlinear Schrödinger limit of the Korteweg-de Vries equation. (English)
[J] Physica D 32, No.1, 83-106 (1988). ISSN 0167-2789

Summary: Using the mutiscale approach of Zakharov and Kuznetsov it is shown that the nonlinear Schrödinger periodic scattering data is related to the Korteweg-de Vries periodic scattering data via an average over the Korteweg-de Vries carrier oscillation. This allows a complete elucidation of the physical meaning of the nonlinear Schrödinger scattering data, conservation laws, theta function solutions and reality constraint.
MSC 2000:
*35Q99 PDE of mathematical physics and other areas
37J35 Completely integrable systems, etc.
37K10 Completely integrable systems etc.

Keywords: nonlinear Schrödinger limit; Korteweg-de Vries equation

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