Hadamard's Problem and Coxeter Groups: New Examples of Huygens' Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 28 (1994) no. 1, pp. 3-15.

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Yu. Yu. Berest; A. P. Veselov. Hadamard's Problem and Coxeter Groups: New Examples of Huygens' Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 28 (1994) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/FAA_1994_28_1_a0/

[1] Petrovskii I. G., Lektsii ob uravneniyakh s chastnymi proizvodnymi, GITTL, M.–L., 1950 | MR

[2] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[3] Adamar Zh., Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Nauka, M., 1978 | MR

[4] Mathisson M., “Le problème de Hadamard relatif à la diffusion des ondes”, Acta Math., 71 (1939), 249–282 | DOI | MR

[5] Asgeirsson L, “Some hints on Huygens' principle and Hadamard's conjecture”, Comm. Pure Appl. Math., 9:3 (1956), 307–327 | DOI | MR

[6] Stellmacher K. L., “Ein Beispiel einer Huygensschen Differentialgleichung”, Nachr. Akad. Wiss. Göttingen Math.–Phys. Kl. IIa, 10 (1953), 133–138 | MR

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

[8] Lagnese J. E., “A solution of Hadamard's problem for a restricted class of operators”, Proc. Amer. Math. Soc., 19 (1968), 981–988 | DOI | MR | Zbl

[9] Darboux G., “Sur la representations sphérique des surfaces”, Compt. Rend., 94 (1882), 1343–1345

[10] Adler M., Moser J., “On a class of polynomials connected with the Korteweg–de Vries equation”, Commun. Math. Phys., 61:1 (1978), 1–30 | DOI | MR | Zbl

[11] Novikov S. P., “Periodicheskaya zadacha dlya uravneniya Kortevega–de Friza. I”, Funkts. analiz i ego pril., 8:3 (1974), 54–66 | MR

[12] Berest Yu. Yu., “Deformations preserving Huygens' principle”, J. Math. Phys., 1993 (to appear) | MR

[13] Berest Yu. Yu., Veselov A. P., “Printsip Gyuigensa i gruppy Kokstera”, UMN, 48:3 (1993), 181–182 | MR | Zbl

[14] Olshanetsky M. A., Perelomov A. M., “Quantum completely integrable systems connected with semisimple Lie algebras”, Lett. Math. Phys., 2 (1977), 7–13 | DOI | MR | Zbl

[15] Olshanetsky M. A., Perelomov A. M., “Quantum integrable systems related to Lie algebras”, Phys. Rep., 94 (1983), 313–404 | DOI | MR

[16] Calogero F., “Solution of the one-dimensional $n$-body problem with quadratic and/or inversely quadratic pair potential”, J. Math. Phys., 12 (1971), 419–436 | DOI | MR

[17] Chalykh O. A., Veselov A. P., “Commutative rings of partial differential operators and Lie algebras”, Commun. Math. Phys., 126 (1990), 597–611 ; Preprint of FIM, ETH, Zürich (1988) | DOI | MR | Zbl

[18] Veselov A. P., Styrkas K. L., Chalykh O. A., “Algebraicheskaya integriruemost dlya uravneniya Shrëdingera i gruppy, porozhdennye otrazheniyami”, TMF, 94:2 (1993), 253–275 | MR | Zbl

[19] Opdam E. M., “Some applications of hypergeometric shift operators”, Invent. Math., 98 (1989), 1–18 | DOI | MR | Zbl

[20] Dunkl C. F., “Differential-difference operators associated to reflection groups”, Trans. Amer. Math. Soc., 311 (1989), 167–183 | DOI | MR | Zbl

[21] Heckman G. J., “A remark on the Dunkl differential-difference operators”, Progr. Math., 101 (1991), 181–191 | DOI | MR | Zbl

[22] Felder G., Veselov A. P., Shift operator for Calogero–Sutherland quantum problems via Knizhnik–Zamolodchikov equation, Preprint FIM, ETH, Zürich (1993) | MR

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

[24] Ibragimov N. Kh., Oganesyan A. O., “Ierarkhiya gyuigensovykh uravnenii v prostranstvakh s netrivialnoi konformnoi gruppoi”, UMN, 46:3 (1991), 111–146 | MR | Zbl

[25] Weiss J., Tabor M., Carnevale G., “The Painlevé property for partial differential equations”, J. Math. Phys., 24 (1983), 522–526 | DOI | MR | Zbl

[26] Weiss J., “The sine-Gordon equation: complete and partial integrability”, J. Math. Phys., 25 (1984), 2226–2235 | DOI | MR | Zbl

[27] Stellmacher K. L., “Eine Klasse Huygensscher Differentialgleichungen und ihre Integration”, Math. Ann., 130:3 (1955), 219–233 | DOI | MR | Zbl

[28] Gelfand I. M., Shilov G. E., Obobschennye funktsii i deistviya nad nimi, GIFML, M., 1959

[29] Bernshtein I. N., Gelfand I. M., Gelfand S. I., “Kletki Shuberta i kogomologii prostranstv $G/P$”, UMN, 28:3 (1973), 3–26 | MR