Abstract
In this paper, we consider an inverse problem for the [Formula: see text]-dimensional random Schrödinger equation [Formula: see text]. We study the scattering of plane waves in the presence of a potential [Formula: see text] which is assumed to be a Gaussian random function such that its covariance is described by a pseudodifferential operator. Our main result is as follows: given the backscattered far field, obtained from a single realization of the random potential [Formula: see text], we uniquely determine the principal symbol of the covariance operator of [Formula: see text]. Especially, for [Formula: see text] this result is obtained for the full nonlinear inverse backscattering problem. Finally, we present a physical scaling regime where the method is of practical importance.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
