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On the nonlinear Schrödinger limit of the Korteweg-de Vries equation. (English) Zbl 0697.35125
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:
35Q99PDE of mathematical physics and other areas
37J35Completely integrable systems, topological structure of phase space, integration methods
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies