Geodesic
Moutard transformation and its application to some physical problems. I. The case of two independent variables
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 100-124 
E. Sh. Gutshabash. Moutard transformation and its application to some physical problems. I. The case of two independent variables. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 100-124. http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a5/
@article{ZNSL_2012_398_a5,
     author = {E. Sh. Gutshabash},
     title = {Moutard transformation and its application to some physical {problems.~I.} {The} case of two independent variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {100--124},
     year = {2012},
     volume = {398},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a5/}
}
TY  - JOUR
AU  - E. Sh. Gutshabash
TI  - Moutard transformation and its application to some physical problems. I. The case of two independent variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 100
EP  - 124
VL  - 398
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a5/
LA  - ru
ID  - ZNSL_2012_398_a5
ER  - 
%0 Journal Article
%A E. Sh. Gutshabash
%T Moutard transformation and its application to some physical problems. I. The case of two independent variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 100-124
%V 398
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a5/
%G ru
%F ZNSL_2012_398_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A general scheme of application of Moutard transformation to the partial differential of the second order with two independent variables is proposed. The realization of this scheme is given for the nonstationary Shrödinger equation and Fokker–Planck equation as well as wave equation and Helmholts equation.

[1] V. B. Matveev, M. A. Salle, Darboux Transformation and Solitons, Springer Series Nonlinear Dynamics, 1991 | DOI | MR

[2] C. Rogers, W. F. Shadwick, Båklund Transformation and Their Applications, Academica, New York, 1982 | MR | Zbl

[3] S. B. Leble, E. V. Doktorov, A Dressing Method in Mathematical Physics, Mathematical Physics Studies, 28, Springer-Verlag, 2007 | MR | Zbl

[4] C. Atorne, J. J. C. Nimmo, Inverse Problems, 28:7 (1991), 808

[5] E. I. Ganzha, 1996, arXiv: solv-int/9606001

[6] E. I. Ganzha, Sib. mat. zh., 42:3 (2000), 541 | MR | Zbl

[7] I. Taimanov, S. Tsarev, Proceeding of the 16th OCU Int. Acad. Symp. (2008), OC Ami Studies, 3, 2009

[8] I. Taimanov, S. Tsarev, 2009, arXiv: ; Современная математика. Фундаментальные направления, 35, 2010, 101 0906.5141v1[math-ph] | MR

[9] E. Sh. Gutshabash, Proceedings Day on Diffraction–2003, St. Petersburg, June, 2003 | Zbl

[10] E. Sh. Gutshabash, M. A. Salle, Proceedings Day on Diffraction–99, St. Petersburg, May, 2001

[11] A. Messia, Kvantovaya mekhanika, v. 1, Nauka, M., 1978 | MR

[12] K. Husimi, Progr. Theor. Phys., 9 (1953), 381 | DOI | MR | Zbl

[13] I. A. Kvasnikov, Termodinamika i statisticheskaya fizika. Teoriya neravnovesnykh sistem, Izd-vo MGU, M., 1987 | MR

[14] S. P. Novikov, A. P. Veselov, DAN SSSR, 279:1 (1984), 20 | MR | Zbl

[15] E. Sh. Gutshabash, V. D. Lipovskii, Zap. nauchn. semin. LOMI, 180, 1990, 53 | MR | Zbl

[16] E. Kamke, Spravochnik po obyknovennym differentsialnym uravneniyam, GIFML, M., 1961

[17] I. N. Vekua, Obobschennye analiticheskie funktsii, Nauka, M., 1988 | MR | Zbl

[18] P. K. Suetin, Ortogonalnye mnogochleny po dvum peremennym, Nauka, M., 1988 | MR | Zbl