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Nonlinear Schrödinger equation on a semi-axis and an inverse problem associated with it

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Abstract

On the semi-axis x⩾0 we consider a matrix nonlinear Schrödinger equation “with attraction.” We give a definition of the Weyl-Titchmarsh function for an auxiliary non-self-adjoint linear system and we solve the inverse problem of recovering the system from its Weyl-Titchmarsh function. A description is given of the evolution of the Weyl-Titchmarsh function.

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Authors and Affiliations

  1. Marine Hydrophysics Institute, Hydroacoustics Branch, Academy of Sciences of the Ukrainian SSR, Odessa

    A. L. Sakhnovich

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  1. A. L. Sakhnovich
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 356–363, March, 1990.

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Sakhnovich, A.L. Nonlinear Schrödinger equation on a semi-axis and an inverse problem associated with it. Ukr Math J 42, 316–323 (1990). https://doi.org/10.1007/BF01057016

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  • DOI: https://doi.org/10.1007/BF01057016

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