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Variational Methods in Nonlinear Field Equations

Solitary Waves, Hylomorphic Solitons and Vortices

  • Book
  • © 2014

Overview

Authors:
  1. Vieri Benci

    1. Dip. di Matematica, Università degli Studi di Pisa, Pisa, Italy

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  2. Donato Fortunato

    1. Dip. di Matematica, Università degli Studi di Bari "Aldo Moro", Bari, Italy

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  • Provides existence and stability results for solitary waves, solitons and vortices in variational nonlinear PDE’s
  • Theory sufficiently general and flexible to be applied to many other situations
  • Applications to the existence of solitons in the nonlinear beam equation and to the study of vortices
  • Contains a general existence theory for hylomorphic solitons
  • Summarizes the main results obtained in the last 35 years
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xix
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  2. The General Principles

    • Vieri Benci, Donato Fortunato
    Pages 1-25

  3. Solitary Waves and Solitons: Abstract Theory

    • Vieri Benci, Donato Fortunato
    Pages 27-59

  4. The Nonlinear Schrödinger Equation

    • Vieri Benci, Donato Fortunato
    Pages 61-110

  5. The Nonlinear Klein-Gordon Equation

    • Vieri Benci, Donato Fortunato
    Pages 111-142

  6. The Nonlinear Klein-Gordon-Maxwell Equations

    • Vieri Benci, Donato Fortunato
    Pages 143-182

  7. The Nonlinear Schrödinger-Maxwell Equations

    • Vieri Benci, Donato Fortunato
    Pages 183-202

  8. The Nonlinear Beam Equation

    • Vieri Benci, Donato Fortunato
    Pages 203-218

  9. Vortices

    • Vieri Benci, Donato Fortunato
    Pages 219-236

  10. Back Matter

    Pages 237-253
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Keywords

About this book

The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.

Reviews

“This book is a useful, enlightening, and thought-provoking exposition of the research and findings over the last 35 years of using and implementing variational techniques to better understand the dynamics of nonlinear field equations. These reviewers would highly recommend this text be on the shelf of any applied mathematician/physicist who uses variational techniques to analyze nonlinear field equations.” (David J. Kaup and Thomas Keith Vogel, Mathematical Reviews, November, 2015)

Authors and Affiliations

  • Dip. di Matematica, Università degli Studi di Pisa, Pisa, Italy

    Vieri Benci

  • Dip. di Matematica, Università degli Studi di Bari "Aldo Moro", Bari, Italy

    Donato Fortunato

Bibliographic Information

  • Book Title: Variational Methods in Nonlinear Field Equations

  • Book Subtitle: Solitary Waves, Hylomorphic Solitons and Vortices

  • Authors: Vieri Benci, Donato Fortunato

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-06914-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Hardcover ISBN: 978-3-319-06913-5Published: 03 November 2014

  • Softcover ISBN: 978-3-319-36122-2Published: 23 August 2016

  • eBook ISBN: 978-3-319-06914-2Published: 24 October 2014

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XIX, 253

  • Topics: Partial Differential Equations, Analysis, Mathematical Physics

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