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

Research paper by A. L. Sakhnovich

Indexed on: 01 Mar '90Published on: 01 Mar '90Published in: Ukrainian Mathematical Journal



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.