The Cauchy Problem for the KdV Equation With Non-Decreasing Initial Data

  • V. A. Marchenko
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)


At the present time there exist numerous modifications of the inverse problem method which can be used to obtain wide classes of solutions of nonlinear equations. However, with the exception of rapidly decreasing and periodic initial data, the applicability of these methods for the solution of the Cauchy problem has not, in fact, been studied.


Verse Vicin 


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  1. 1.
    V. Bargman: “On the connection between phase shifts and scattering potential” Rev. Mod. Phys., 30-45 (1949).Google Scholar
  2. 2.
    I.S. Katz: “The spectrum of the differential operator,” Izv. Akad. Nauk. SSSR Ser. Mat., 27, 1081–1112 (1963).MathSciNetGoogle Scholar
  3. 3.
    D.S. Lundina: “Compactness of the set of reflectionless potentials,” Teoriya funktsyi, funkt-syonal’nyi analiz i ikh prilozheniya, 44, 57–66 (1985).MATHGoogle Scholar
  4. 4.
    V.A. Marchenko: Nonlinear Equations and Operator Algebras (D. Reidel, Dordrecht 1987).Google Scholar

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© Springer-Verlag Berlin Heidelberg 1991

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  • V. A. Marchenko

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