Geodesic
The dressing method and separation of variables: The two-dimensional case
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 327-331 Cet article a éte moissonné depuis la source Math-Net.Ru

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Separation of variables is very convenient for obtaining solutions of linear differential equations in explicit form. We use the dressing method to widen the class of such equations. As an example, we dress a two-dimensional linear differential operator, including an operator with constant coefficients.
Keywords: separation of variables, dressing method, Schrödinger operator. 
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V. G. Marikhin. The dressing method and separation of variables: The two-dimensional case. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 327-331. http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a2/

[1] G. Darboux, Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal. Première partie. Généralités. Coordonnées curvilignes. Surfaces minima, Reimpression de la deuxieme edition de 1914, Chelsea, New York, 1972 | MR | Zbl

[2] A. B. Shabat, TMF, 103:1 (1995), 170–175 | DOI | MR | Zbl

[3] E. V. Ferapontov, A. P. Veselov, J. Math. Phys., 42:2 (2001), 590–607 | DOI | MR | Zbl

[4] I. A. Taimanov, S. P. Tsarev, TMF, 157:2 (2008), 188–207 | DOI | MR | Zbl

[5] M. A. Skvortsov, P. M. Ostrovskii, Pisma v ZhETF, 85:1 (2007), 79–83 | DOI

[6] W. Miller Jr., Symmetry and Separation of Variables, Encyclopedia Math. Appl., 4, Addison-Wesley, Reading, MA, 1977 | MR | Zbl