Iso-Huygens Deformations of Homogeneous Differential Operators Related to a Special Cone of Rank~3
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 927-940.

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

We consider iso-Huygens deformations of homogeneous hyperbolic Gindikin operators related to a special cone of rank 3. The deformations are carried out with the use of Stellmacher–Lagnese and Calogero–Moser potentials. Using the notion of gauge equivalence of operators and the algebraic method of intertwining operators, we write out the fundamental solutions of the deformed operators in closed form and give sufficient conditions for the Huygens principle to hold for these operators in the strengthened or ordinary form.
@article{MZM_2001_70_6_a10,
     author = {S. P. Khekalo},
     title = {Iso-Huygens {Deformations} of {Homogeneous} {Differential} {Operators} {Related} to a {Special} {Cone} of {Rank~3}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {927--940},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a10/}
}
TY  - JOUR
AU  - S. P. Khekalo
TI  - Iso-Huygens Deformations of Homogeneous Differential Operators Related to a Special Cone of Rank~3
JO  - Matematičeskie zametki
PY  - 2001
SP  - 927
EP  - 940
VL  - 70
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a10/
LA  - ru
ID  - MZM_2001_70_6_a10
ER  - 
%0 Journal Article
%A S. P. Khekalo
%T Iso-Huygens Deformations of Homogeneous Differential Operators Related to a Special Cone of Rank~3
%J Matematičeskie zametki
%D 2001
%P 927-940
%V 70
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a10/
%G ru
%F MZM_2001_70_6_a10
S. P. Khekalo. Iso-Huygens Deformations of Homogeneous Differential Operators Related to a Special Cone of Rank~3. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 927-940. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a10/

[1] Gindikin S. G., “Analiz v odnorodnykh oblastyakh”, UMN, 19:4 (1964), 3–92 | MR | Zbl

[2] Vainberg B. R., Gindikin S. G., “Ob usilennom printsipe Gyuigensa dlya odnogo klassa differentsialnykh operatorov s postoyannymi koeffitsientami”, Tr. MMO, 16, URSS, M., 1967, 151–180 | MR | Zbl

[3] Garding L., “The solution of Cauchy's problem for two totally hyperbolic differential equations by means of Riesz integrals”, Ann. Math., 48:4 (1947), 785–826 | DOI | MR | Zbl

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

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

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

[7] Gindikin S. G., “Zadacha Koshi dlya silno odnorodnykh differentsialnykh operatorov”, Tr. MMO, 16, URSS, M., 1967, 181–208 | MR | Zbl

[8] 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 | MR | Zbl

[9] Burchnall J. L., Chaundy T. W., “A set of differential equations, which can be solved by polynomials”, Proc. London Math. Soc., 30 (1929–1930), 401–414 | DOI

[10] Demidov E. E., Ierarkhiya Kadomtseva–Petrashvili i problema Shottki. Spetsialnyi kurs, MK NMU, M., 1995

[11] Khekalo S. P., “Fundamentalnoe reshenie iterirovannogo operatora tipa Keli–Gordinga”, UMN, 55:3 (2000), 191–192 | MR | Zbl