Geodesic
Difference Schr\"odinger equation and quasisymmetric polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 200-211

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We study the singularity of solutions of the Schrödinger equation with a finite potential at the point $k=0$. In the case of delta-type potentials, we show that the nature of this singularity is automodel in a certain sense. We discuss using the obtained results to construct an approximate solution of the inverse scattering problem on the whole axis. For this, we introduce the concept of a quasisymmetric polynomial associated with a given curve.
Keywords: Schrödinger operator, Green's function, additional spectrum, difference model. 
@article{TMF_2015_184_2_a1,
     author = {A. B. Shabat},
     title = {Difference {Schr\"odinger} equation and quasisymmetric polynomials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {200--211},
     publisher = {mathdoc},
     volume = {184},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a1/}
}
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A. B. Shabat. Difference Schr\"odinger equation and quasisymmetric polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 200-211. http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a1/