@article{TRSPY_2018_302_a15,
author = {R. G. Novikov and I. A. Taimanov},
title = {Darboux{\textendash}Moutard transformations and {Poincar\'e{\textendash}Steklov} operators},
journal = {Informatics and Automation},
pages = {334--342},
year = {2018},
volume = {302},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_302_a15/}
}
R. G. Novikov; I. A. Taimanov. Darboux–Moutard transformations and Poincaré–Steklov operators. Informatics and Automation, Topology and physics, Tome 302 (2018), pp. 334-342. http://geodesic.mathdoc.fr/item/TRSPY_2018_302_a15/
[1] Adilkhanov A. N., Taimanov I. A., “On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential”, Commun. Nonlinear Sci. Numer. Simul., 42 (2017), 83–92 | DOI | MR
[2] Crum M. M., “Associated Sturm–Liouville systems”, Q. J. Math., 6 (1955), 121–127 | DOI | MR
[3] Darboux G., “Sur une proposition relative aux équations linéaires”, C. r. Acad. sci. Paris., 94 (1882), 1456–1459
[4] B. A. Dubrovin, I. M. Kričever, S. P. Novikov, “The Schrödinger equation in a periodic field and Riemann surfaces”, Sov. Math., Dokl., 17 (1976), 947–951 | MR
[5] P. G. Grinevich, R. G. Novikov, “Generalized analytic functions, Moutard-type transforms, and holomorphic maps”, Funct. Anal. Appl., 50:2 (2016), 150–152 | DOI | DOI | MR
[6] Grinevich P. G., Novikov R. G., “Moutard transform approach to generalized analytic functions with contour poles”, Bull. sci. math., 140:6 (2016), 638–656 | DOI | MR
[7] Grinevich P. G., Novikov R. G., “Moutard transform for generalized analytic functions”, J. Geom. Anal., 26:4 (2016), 2984–2995 | DOI | MR
[8] Grinevich P. G., Novikov R. G., Moutard transform for the conductivity equation, 2018, arXiv: 1801.00295 [math-ph] | MR
[9] P. G. Grinevich, S. P. Novikov, “Two-dimensional ‘inverse scattering problem’ for negative energies and generalized-analytic functions. I: Energies below the ground state”, Funct. Anal. Appl., 22:1 (1988), 19–27 | DOI | MR
[10] Hu H.-C., Lou S.-Y., Liu Q.-P., “Darboux transformation and variable separation approach: the Nizhnik–Novikov–Veselov equation”, Chin. Phys. Lett., 20:9 (2003), 1413–1415 | DOI
[11] R. M. Matuev, I. A. Taimanov, “The Moutard transformation of two-dimensional Dirac operators and the conformal geometry of surfaces in four-dimensional space”, Math. Notes, 100:6 (2016), 835–846 | DOI | DOI | MR
[12] Matveev V. B., “Darboux transformations, covariance theorems and integrable systems”, L. D. Faddeev's seminar on mathematical physics, AMS Transl. Ser. 2, 201, Amer. Math. Soc., Providence, RI, 2000, 179–209 | MR
[13] Matveev V. B., Salle M. A., Darboux transformations and solitons, Springer, Berlin, 1991 | MR
[14] Moutard Th., “Sur la construction des équations de la forme $\frac {1}{z}\frac {d^2 z}{dx dy} = \lambda (x,y)$, qui admettent une intégrale générale explicite”, J. Éc. Polytech., 28 (1878), 1–11
[15] R. G. Novikov, I. A. Taimanov, “The Moutard transformation and two-dimensional multipoint delta-type potentials”, Russ. Math. Surv., 68:5 (2013), 957–959 | DOI | DOI | MR
[16] R. G. Novikov, I. A. Taimanov, “Moutard type transformation for matrix generalized analytic functions and gauge transformations”, Russ. Math. Surv., 71:5 (2016), 970–972 | DOI | DOI | MR
[17] R. G. Novikov, I. A. Taimanov, S. P. Tsarev, “Two-dimensional von Neumann–Wigner potentials with a multiple positive eigenvalue”, Funct. Anal. Appl., 48:4 (2014), 295–297 | DOI | DOI | MR
[18] I. A. Taimanov, “The Moutard transformation of two-dimensional Dirac operators and Möbius geometry”, Math. Notes, 97:1 (2015), 124–135 | DOI | DOI | MR
[19] I. A. Taimanov, “A fast decaying solution to the modified Novikov–Veselov equation with a one-point singularity”, Dokl. Math., 91:1 (2015), 35–36 | DOI | MR
[20] I. A. Taimanov, “Blowing up solutions of the modified Novikov–Veselov equation and minimal surfaces”, Theor. Math. Phys., 182:2 (2015), 173–181 | DOI | DOI | MR
[21] I. A. Taimanov, S. P. Tsarev, “Two-dimensional Schrödinger operators with fast decaying potential and multidimensional $L_2$-kernel”, Russ. Math. Surv., 62:3 (2007), 631–633 | DOI | DOI | MR
[22] I. A. Taimanov, S. P. Tsarev, “Blowing up solutions of the Novikov–Veselov equation”, Dokl. Math., 77:3 (2008), 467–468 | DOI | MR
[23] I. A. Taimanov, S. P. Tsarev, “Two-dimensional rational solitons and their blowup via the Moutard transformation”, Theor. Math. Phys., 157:2 (2008), 1525–1541 | DOI | DOI | MR
[24] I. A. Taimanov, S. P. Tsarev, “On the Moutard transformation and its applications to spectral theory and soliton equations”, J. Math. Sci., 170:3 (2010), 371–387 | DOI | MR
[25] I. A. Taimanov, S. P. Tsarev, “Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation”, Theor. Math. Phys., 176:3 (2013), 1176–1183 | DOI | DOI | MR
[26] A. P. Veselov, S. P. Novikov, “Finite-zone, two-dimensional, potential Schrödinger operators. Explicit formulas and evolution equations”, Sov. Math., Dokl., 30 (1984), 588–591 | MR | MR
[27] A. P. Veselov, S. P. Novikov, “Finite-zone, two-dimensional Schrödinger operators. Potential operators”, Sov. Math., Dokl., 30 (1984), 705–708 | MR
[28] Yu D., Liu Q. P., Wang S., “Darboux transformation for the modified Veselov–Novikov equation”, J. Phys. A: Math. Gen., 35:16 (2002), 3779–3785 | DOI | MR