Constructively Factoring Linear Partial Differential Operators in Two Variables |
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Authors: | R Beals E A Kartashova |
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Institution: | (1) Yale University, New Haven, Connecticut, USA;(2) Johannes Kepler Universitat (JKU) Linz, Linz, Austria |
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Abstract: | We study conditions under which a partial differential operator of arbitrary order n in two variables or an ordinary linear
differential operator admits a factorization with a first-order factor on the left.The process of factoring consists of recursively
solving systems of linear equations subject to certain differential compatibility conditions.In the general case of partial
differential operators, it is not necessary to solve a differential equation. In special degenerate cases, such as an ordinary
differential operator, the problem eventually reduces to solving some Riccati equation(s). We give the factorization conditions
explicitly for the second and third orders and in outline form for higher orders.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 165–180, November, 2005. |
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Keywords: | differential operators factorization of differential operators algebraic factorization |
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