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On the reduction of the degree of linear differential operators

Authors :
Bobieński, Marcin
Gavrilov, Lubomir
Source :
Nonlinearity 24 (2011) 373-388
Publication Year :
2010

Abstract

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type.

Details

Database :
arXiv
Journal :
Nonlinearity 24 (2011) 373-388
Publication Type :
Report
Accession number :
edsarx.1003.0629
Document Type :
Working Paper
Full Text :
https://doi.org/10.1088/0951-7715/24/2/002