Disorder and Nonlinearity

Proceedings of the Workshop J.R. Oppenheimer Study Center Los Alamos, New Mexico, 4–6 May, 1988

  • Alan R. Bishop
  • David K. Campbell
  • Stephanos Pnevmatikos
Conference proceedings

Part of the Springer Proceedings in Physics book series (SPPHY, volume 39)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Localization and Nonlinearity

  3. Solitons and Disorder

    1. Front Matter
      Pages 77-77
    2. Y. S. Kivshar, A. M. Kosevich, A. O. Chubykalo
      Pages 78-84
    3. P. J. Pascual, L. Vazquez, S. Pnevmatikos, A. R. Bishop
      Pages 85-92
    4. F. K. Abdullaev, S. A. Darmanyan
      Pages 93-101
    5. G. P. Tsironis, S. Pnevmatikos, P. S. Lomdahl
      Pages 102-108
  4. Scattering and Localization

    1. Front Matter
      Pages 109-109
    2. G. Papanicolaou, M. Postel, P. Sheng, B. White
      Pages 110-116
    3. F. C. MacKintosh, Sajeev John
      Pages 117-126
    4. S. Chelkowski, A. D. Bandrauk
      Pages 134-139
  5. Postscript

    1. Front Matter
      Pages 141-141

About these proceedings

Introduction

ill the past three decades there has been enonnous progress in identifying the es­ sential role that "nonlinearity" plays in physical systems. Classical nonlinear wave equations can support localized, stable "soliton" solutions, and nonlinearities in quantum systems can lead to self-trapped excitations, such as polarons. Since these nonlinear excitations often dominate the transport and response properties of the systems in which they exist, accurate modeling of their effects is essential to interpreting a wide range of physical phenomena. Further, the dramatic de­ velopments in "deterministic chaos", including the recognition that even simple nonlinear dynamical systems can produce seemingly random temporal evolution, have similarly demonstrated that an understanding of chaotic dynamics is vital to an accurate interpretation of the behavior of many physical systems. As a conse­ quence of these two developments, the study of nonlinear phenomena has emerged as a subject in its own right. During these same three decades, similar progress has occurred in understand­ ing the effects of "disorder". Stimulated by Anderson's pioneering work on "dis­ ordered" quantum solid state materials, this effort has also grown into a field that now includes a variety of classical and quantum systems and treats "disorder" arising from many sources, including impurities, random spatial structures, and stochastic applied fields. Significantly, these two developments have occurred rather independently, with relatively little overlapping research.

Keywords

Disorder Localization Nonlinearity Solitons chaos deterministic chaos dynamics electron fields hydrogen scattering soliton structure

Editors and affiliations

  • Alan R. Bishop
    • 1
  • David K. Campbell
    • 1
  • Stephanos Pnevmatikos
    • 1
  1. 1.Los Alamos National LaboratoryCenter of Nonlinear StudiesLos AlamosUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-74893-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-74895-0
  • Online ISBN 978-3-642-74893-6
  • Series Print ISSN 0930-8989
  • Series Online ISSN 1867-4941
  • About this book