Abstract
Using new developments in the theory of traces, determinants, and elementary operators on quasi-Banach operator ideals we clarify and extend Marchenko’s method for realizing solutions of the KdV equation. Moreover, we point out why abstract traces and determinants on quasi-Banach operator ideals are appropriate tools for obtaining solutions of the KdV equation. The method we present can also be applied to other nonlinear equations in soliton physics.
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