Abstract
In this note we consider the problem of representing solutions of linear partial differential equations with two independent variables in the form of finite sums. We obtain one sufficient representability criterion and indicate several classes of equations to which it is applicable. As examples we obtain new exact solutions of the transformed minimal surface equation and the Tricomi equation.
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E. Kamke, Handbook of Ordinary Differential Equations [Russian translation], Nauka, Moscow (1971).
F. Tricomi, Linear Equations of Mixed Type [Russian translation], Gostekhizdat, Moscow (1947).
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Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 359–363, September, 1976.
In conclusion, the author would like to thank A. F. Sidorov for his guidance.
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Titov, S.S. Representation of solutions of linear partial differential equations in the form of finite sums. Mathematical Notes of the Academy of Sciences of the USSR 20, 760–763 (1976). https://doi.org/10.1007/BF01097245
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DOI: https://doi.org/10.1007/BF01097245