An algorithm of obtaining partial solutions of linear differential equations in partial derivatives that admit certain nontrivial symmetry algebra but are nonintegrable by the standard methods is described. The notion of degenerate solution is introduced. Natural classification of solutions is suggested.
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References
V. N. Shapovalov, Diff. Uravn., 16, No. 10, 1864–1874 (1980).
A. V. Shapovalov and I. V. Shirokov, Teor. Matem. Fiz., 104, No. 2, 195–213 (1995).
A. V. Shapovalov and I. V. Shirokov, Teor. Matem. Fiz., 106, 13–15 (1996).
I. V. Shirokov, K-orbits, harmonic analysis on homogeneous spaces, and integration of differential equations [in Russian], Preprint, Omsk State University, Omsk (1998).
A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1978).
V. G. Fedoseev, A. V. Shapovalov, and I. V. Shirokov, Sov. Phys. J., No. 9, 777–780 (1991).
O. L. Varaksin, V. V. Firstov, A. V. Shapovalov, and I. V. Shirokov, Russ. Phys. J., No. 5, 508–512 (1995).
S. P. Baranovskii and I. V. Shirokov, Sib. Matem. Zh., 50, No. 4, 737–745 (2009).
I. V. Shirokov, Teor. Matem. Fiz., 126, No. 3, 393–408 (2001).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 20–26, May, 2011.
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Goncharovskii, M.M., Shirokov, I.V. Classification of degenerate solutions of linear differential equations. Russ Phys J 54, 527–535 (2011). https://doi.org/10.1007/s11182-011-9649-5
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DOI: https://doi.org/10.1007/s11182-011-9649-5