Alexander Sakhnovich 2008 Inverse Problems 24 025026 doi:10.1088/0266-5611/24/2/025026
Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation
Alexander Sakhnovich
Show affiliationsA Borg–Marchenko-type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve the inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by a new and simple sufficient condition on the potential, which implies this asymptotic condition. The evolution of the Weyl function is discussed and the solution of an initial-boundary-value problem for the N-wave equation follows. Explicit solutions of an inverse problem are obtained. The system with a shifted argument is treated.
- PACS
- MSC
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78A46 Inverse scattering problems
34B20 Weyl theory and its generalizations
78A60 Lasers, masers, optical bistability, nonlinear optics (See also 81V80)
- Subjects
- Dates
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Issue 2 (April 2008)
Received 17 July 2007, in final form 25 February 2008
Published 17 March 2008
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Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation
Alexander Sakhnovich 2008 Inverse Problems 24 025026
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