Floquet Theory for Partial Differential Equations

  • Peter Kuchment
Part of the Operator Theory: Advances and Applications book series (OT, volume 60)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Peter Kuchment
    Pages 1-89
  3. Peter Kuchment
    Pages 91-102
  4. Peter Kuchment
    Pages 125-186
  5. Peter Kuchment
    Pages 187-262
  6. Peter Kuchment
    Pages 263-302
  7. Back Matter
    Pages 303-354

About this book

Introduction

Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111­ 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103­ 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].

Keywords

Boundary value problem Complex analysis Theoretical physics evolution ordinary differential equation partial differential equation scattering theory

Authors and affiliations

  • Peter Kuchment
    • 1
  1. 1.Department of Mathematics and StatisticsWichita State UniversityWichitaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-8573-7
  • Copyright Information Birkhäuser Verlag 1993
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-9686-3
  • Online ISBN 978-3-0348-8573-7