Abstract
For linear problems which are associated with known, exactly integrable nonlinear evolution equations, one gives the corresponding integrodifferential Λ-operators. Relative to the expansions with respect to the elgenfunctions of Λ-operators, the method of the inverse scattering problem can be considered as the analog of the Fourier transform of linear problems, while the Λ-operators are the analogues of the differentiation operator. One considers the equations: Koteweg-de Vries, the nonlinear Schrödinger equations, the nonlinear Schrödinger equations with a derivative, the system of three waves, the matricial analog of the KdV equation, the Toda chain equation.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 96, pp. 105–112, 1980.
We express our thanks to L. D. Faddeev, S. V. Manakov, A. G. Reiman, L. A. Takhtadzhyan, and V. S. Gerdzhikov, the discussions with whom have furthered our understanding of the special role of the Λ -operator.
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Kulish, P.P. Generating operators for integrable nonlinear evolution equations. J Math Sci 21, 718–723 (1983). https://doi.org/10.1007/BF01094435
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DOI: https://doi.org/10.1007/BF01094435