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Inverse scattering on the line for a generalized nonlinear Schrödinger equation. (English) Zbl 1063.34006

The inverse scattering problem is studied for the nonlinear differential equation \[ -u''+Q(x,u)u=k^2 u \] on the line. The unique recovery of the potential is established from a set of scattering data.

MSC:

34A55 Inverse problems involving ordinary differential equations
34L25 Scattering theory, inverse scattering involving ordinary differential operators
34L30 Nonlinear ordinary differential operators
47E05 General theory of ordinary differential operators
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