Matrix differential equations of the second order
Abstract
A matrix differential equation of second order which appears in multichannel problems of the quantum theory of scattering and in boundary value problems in the theory of waveguides is considered. The properties of the solutions of the equation are determined, and with their aid Green's functions for fundamental waveguide problems are constructed. The Cauchy problem is solved by means of transformation operators. Sufficient conditions for the existence of transformation operators preserving the asymptotic behavior of the solutions at infinity are obtained.
 Publication:

Differentsialnye Uravneniia
 Pub Date:
 April 1977
 Bibcode:
 1977DnU....13..579A
 Keywords:

 Boundary Value Problems;
 Differential Equations;
 Quantum Theory;
 S Matrix Theory;
 Waveguides;
 Cauchy Problem;
 Green'S Functions;
 Operators (Mathematics);
 Physics (General)