Geodesic
On an inverse dynamic problem for the wave equation with a~potential on a~real line
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 212-231

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We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator (dynamic Dirichlet-to-Neumann map). We derive equations of inverse problem and also point out the relationship between dynamic inverse problem and spectral inverse problem from a matrix-valued measure. 
@article{ZNSL_2017_461_a11,
     author = {A. S. Mikhaylov and V. S. Mikhaylov},
     title = {On an inverse dynamic problem for the wave equation with a~potential on a~real line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {212--231},
     publisher = {mathdoc},
     volume = {461},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a11/}
}
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A. S. Mikhaylov; V. S. Mikhaylov. On an inverse dynamic problem for the wave equation with a~potential on a~real line. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 212-231. http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a11/