Fixed energy problem for nonlinear Schrödinger operator
1Professor of applied mathematics, University of Oulu, Finland
|Online Access:||PDF Full Text (PDF, 0.3 MB)|
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2019052717116
|Publish Date:|| 2019-05-27
This work studies the inverse fixed energy scattering problem for the generalised nonlinear Schrödinger operators. We prove that in a three-dimensional case the unknown compactly supported generalised nonlinear potential (with some restriction for this potential) from L 2 space can be uniquely determined by the scattering data with fixed positive energy (meaning that we have the knowledge of the scattering amplitude with fixed non-zero spectral parameter). The results are based on the new estimates for the Faddeev's Green function in L ∞. These results may have applications in nonlinear optics for the saturation model. In particular, the constant coefficients of this model can be uniquely reconstructed by the scattering data with fixed energy.
Journal of physics. Conference series
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
This work was supported by the Academy of Finland (Finnish Programme for Centres of Excellence in Research, Inverse Modelling and Imaging, no. 312123, 2018-2025).
|Academy of Finland Grant Number:||
312123 (Academy of Finland Funding decision)
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