Geodesic
Solutions of two-dimensional Schr\"odinger-type equations in a~magnetic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 2, pp. 219-226

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We use the method of dressing by a linear operator of general form to construct new solutions of Schrödinger-type two-dimensional equations in a magnetic field. In the case of a nonunit metric, we integrate the class of solutions that admit a variable separation before dressing. In particular, we show that the ratio of the coefficients of the differential operators in the unit metric case satisfies the Hopf equation. We establish a relation between the solutions of the two-dimensional eikonal equation with the unit right-hand side and solutions of the Hopf equation.
Keywords: dressing method, quantum operators, Hopf equation
Mots-clés : eikonal equation. 
@article{TMF_2011_168_2_a2,
     author = {V. G. Marikhin},
     title = {Solutions of two-dimensional {Schr\"odinger-type} equations in a~magnetic field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {219--226},
     publisher = {mathdoc},
     volume = {168},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a2/}
}
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V. G. Marikhin. Solutions of two-dimensional Schr\"odinger-type equations in a~magnetic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 2, pp. 219-226. http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a2/