Singular degree of a rational matrix pseudodifferential operator
Abstract
In our previous work we studied minimal fractional decompositions of a rational matrix pseudodifferential operator: H=A/B, where A and B are matrix differential operators, and B is nondegenerate of minimal possible degree deg(B). In the present paper we introduce the singular degree sdeg(H)=deg(B), and show that for an arbitrary rational expression H=sum_a (A^a_1)/(B^a_1)...(A^a_n)/(B^a_n), we have that sdeg(H) is less than or equal to sum_{a,i} deg(B^a_i). If the equality holds, we call such an expression minimal. We study the properties of the singular degree and of minimal rational expressions. These results are important for the computations involved in the LenardMagri scheme of integrability.
 Publication:

arXiv eprints
 Pub Date:
 August 2013
 DOI:
 10.48550/arXiv.1308.2647
 arXiv:
 arXiv:1308.2647
 Bibcode:
 2013arXiv1308.2647C
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 35S05 (Primary) 16S32;
 13N10 (Secondary)
 EPrint:
 33 pages