Geodesic
Stepwise Gauge Equivalence of Differential Operators
Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 917-929.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study the relation between the notion of gauge equivalence and solutions of certain systems of nonlinear partial differential equations. This relation is based on stepwise gauge equivalence. 
@article{MZM_2005_77_6_a9,
     author = {S. P. Khekalo},
     title = {Stepwise {Gauge} {Equivalence} of {Differential} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {917--929},
     publisher = {mathdoc},
     volume = {77},
     number = {6},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a9/}
}
TY  - JOUR
AU  - S. P. Khekalo
TI  - Stepwise Gauge Equivalence of Differential Operators
JO  - Matematičeskie zametki
PY  - 2005
SP  - 917
EP  - 929
VL  - 77
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a9/
LA  - ru
ID  - MZM_2005_77_6_a9
ER  - 
%0 Journal Article
%A S. P. Khekalo
%T Stepwise Gauge Equivalence of Differential Operators
%J Matematičeskie zametki
%D 2005
%P 917-929
%V 77
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a9/
%G ru
%F MZM_2005_77_6_a9
S. P. Khekalo. Stepwise Gauge Equivalence of Differential Operators. Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 917-929. http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a9/

[1] Berest Yu. Yu., Veselov A. P., “Printsip Gyuigensa i integriruemost”, UMN, 49:6 (1994), 8–78 | MR

[2] Berest Y., “The problem of lacunas and analysis on root systems”, Trans. Amer. Math. Soc., 352:8 (2000), 3743–3776 | DOI | MR | Zbl

[3] Stellmacher K. L., “Ein Beispeil einer Huygennchen Differentialgleichung”, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl., 10 (1953), 133–138 | MR

[4] Lagnese J. E., Stellmacher K. L., “A method of generating classes of Huygens' operators”, J. Math. Mech., 17:5 (1967), 461–472 | MR | Zbl

[5] Berest Y., Molchanov Y., “Fundamental solution for partial differential equations with reflection group invariance”, J. Math. Phys., 36:8 (1995), 4324–4339 | DOI | Zbl

[6] Berest Yu. Yu., Veselov A. P., “Problema Adamara i gruppy Kokstera: novye primery gyuigensovykh uravnenii”, Funktsion. analiz i ego prilozh., 28:1 (1994), 3–15

[7] Berest Y., “Hierarchies of Huygens' operators and Hadamard's conjecture”, Acta Appl. Math., 53 (1998), 125–185 | DOI | MR | Zbl

[8] Babich V. M., “Anzatts Adamara, ego analogi, obobscheniya, prilozheniya”, Algebra i analiz, 3:5 (1991), 1–37

[9] Wilson G., “Bispectral commutative ordinary differential operators”, J. Reine Angew. Math., 442 (1993), 177–204 | Zbl

[10] Berest Y. Y., Loutsenko I. M., “Huygens' principle in Minkowski spaces and soliton solutions of the Korteweg–de Vries equation”, Comm. Math. Phys., 190 (1997), 113–132 | DOI | Zbl

[11] Berest Y., “Solution of a restricted Hadamard problem on Minkowski spaces”, Comm. Pure. Appl. Math., 50 (1997), 1019–1052 | 3.0.CO;2-F class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | Zbl

[12] Khekalo S., “The gauge relation of differential operators and Huygens' principle”, Day on Diffraction, Saint-Petersburg, 2002, 32–34

[13] Khekalo S. P., “Kalibrovochnaya ekvivalentnost differentsialnykh operatorov v chastnykh proizvodnykh”, Mezhdunarodnaya konferentsiya po differentsialnym uravneniyam i dinamicheskim sistemam, Tezisy dokl., Suzdal, 2002, 138–140

[14] Khekalo S., “The gauge related differential operators”, Day on Diffraction, Saint-Petersburg, 2003, 42–43

[15] Khekalo S. P., “Izogyuigensovy deformatsii odnorodnykh differentsialnykh operatorov, svyazannykh so spetsialnym konusom ranga tri”, Matem. zametki, 70:6 (2001), 927–940 | Zbl

[16] Khekalo S. P., “Potentsialy Rissa v prostranstve pryamougolnykh matrits i izogyuigensova deformatsiya operatora Keli–Laplasa”, Dokl. RAN, 376:2 (2001), 168–170 | Zbl