@**article**{RISC2355,author = {R. Beals and E. Kartashova},

title = {{Constructively factoring linear partial differential operators in two variables}},

language = {english},

abstract = {We study conditions under which a partial differential operator of
arbitrary order $n$ in two variables or ordinary linear
differential operator admits a factorization with a first-order
factor on the left. The factorization process consists of solving,
recursively, systems of linear equations, subject to certain
differential compatibility conditions. In the generic case of
partial differential operators one does not have to solve a
differential equation. In special degenerate cases, such as
ordinary differential, the problem is finally reduced to the
solution of some Riccati equation(s). The conditions of
factorization are given explicitly for second- and, and an outline
is given for the higher-order case.
},

journal = {TMPh (Journal of Theoretical and Mathematical Physics)},

volume = {145},

number = {2},

pages = {1510--1523},

publisher = {Springer},

isbn_issn = {ISSN: 0040-5779 (print), 1573-9333 (electronic)},

year = {2005},

month = {November},

refereed = {yes},

keywords = {differential operators, factorization of differential operators, algebraic operators},

length = {14},

url = { http://dx.doi.org/10.1007/s11232-005-0178-7}

}