Ubiquity of the Sturm-Liouville problem in multilayer systems Articles uri icon

authors

  • PÉREZ ÁLVAREZ, ROLANDO
  • PERNAS SALOMON, RENE

published in

  • EPL  Journal

publication date

  • July 2016

start page

  • 10010

issue

  • 1

volume

  • 115

International Standard Serial Number (ISSN)

  • 0295-5075

Electronic International Standard Serial Number (EISSN)

  • 1286-4854

abstract

  • We postulate a general Lagrangian density which leads to the equations of motion of the well-known cases of the electromagnetic field, the theory of elasticity, and some other particular problems in classical physics. When the mentioned cases are studied in multilayer systems, i.e., when the constitutive parameters depend on one of the Cartesian coordinates, all of them lead us to a matrix Sturm-Liouville problem whose equation of motion, in its most general form, can be derived from the postulated Lagrangian density too. These results demonstrate the ubiquitous character of the Sturm-Liouville matrix problem and consequently the relevance of its study from the mathematical, physical and numerical point of view. The consequences of this curious result are briefly analyzed.

subjects

  • Physics