Abstract
Relations between the coefficients of gauge-related deformations and the solutions of a certain system of ordinary nonlinear differential equations are studied. These coefficients are found in an explicit form. Bibliography: 14 titles.
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REFERENCES
Y. Berest and Y. Molchanov, “Fundamental solution for partial differential equations with reflection group invariance,” J. Math. Phis., 36(8), 4324–4339 (1995).
Yu. Yu. Berest and A. P. Veselov, “Huygens' principle and integrability,” Usp. Mat. Nauk, 49, 6(300), 8–78 (1994).
Y. Berest, “Hierarchies of Huygens' operators and Hadamard's conjecture,” Acta Appl. Math., 53, 125–185 (1998).
Y. Berest, “Solution of a restricted Hadamard problem on Minkowski spaces,” Comm. Pure Appl. Math., 50, 1019–1052 (1997).
Y. Y. Berest and I. M. Loutsenko, “Huygens' principle in Minkowski spaces and soliton solutions of the Korteweg-de Vries equation,” Commun. Math. Phys., 190, 113–132 (1997).
Y. Berest, “The problem of lacunas and analysis on root systems,” Trans. Amer. Math. Soc., 352, No.8, 3743–3776 (2000).
G. Wilson, “Bispectral commutative ordinary differential operators,” J. Reine Angew. Math., 442, 177–204 (1993).
S. P. Khekalo, “Fundamental solution for an iterated operator of the Cayley-Garding type,” Usp. Mat. Nauk, 55, No.3, 191–192 (2000).
A. I. Komech, “Linear differential equations in partial derivatives with constant coefficients,” Itogi Nauki Tekhn., 31, 127–261 (1988).
S. P. Khekalo, “The gauge relation of differential operators in partial derivatives,” in: International Conference on Differential Equations and Dynamical Systems, Abstracts, Suzdal (2002), pp. 138–140.
K. L. Stellmacher, “Ein Beispiel einer Huygennchen Differentialgleichung,” Nachr. Akad. Wiss., Gottingen Math. Phis. Kl. Pa., 10, 133–138 (1953).
S. Khekalo, “The gauge relation of differential operators and Huygens' principle, in: Day on Diffraction, St. Petersburg (2002), pp. 32–34.
G. P. Gavrilov and A. A. Sapozhenko, Problems in Discrete Mathematics [in Russian], Nauka, Moscow (1977).
S. P. Khekalo, “Iso-Huygens deformations of homogeneous differential operators associated with a special cone of rank 3,” Mat. Zametki, 70, No.6, 927–940 (2001).
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Dedicated to P. V. Krauklis on the occasion of his seventieth birthday
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 235–251.
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Khekalo, S.P. Gauge-Related Deformations of Ordinary Linear Differential Operators with Constant Coefficients. J Math Sci 132, 136–145 (2006). https://doi.org/10.1007/s10958-005-0482-7
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DOI: https://doi.org/10.1007/s10958-005-0482-7