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Limits of soliton solutions. (English) Zbl 0811.35122
The authors consider the $$N$$-soliton solution to the Korteweg-de Vries equation in the limit $$N \to \infty$$ by careful investigation of the spectral and scattering properties of the Schrödinger operator associated to the KdV equation by the inverse scattering transform. The methods of the paper are applicable to general integrable systems such as the AKNS-class, the Toda lattice, and the Kadomtsev-Petviashvili equation.

MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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