Skip to main content
SpringerLink
Log in

A Unitarian Approach to Classical Electrodynamics: The Semilinear Maxwell Equations

  • Chapter
Contributions to Nonlinear Analysis

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 66))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benci V., Fortunato D., Towards a unified field theory for classical electrodynamics, Arch. Rat. Mech. Anal. 173 (2004), 379–414.

    Article  MATH  Google Scholar 

  2. Benci V., Fortunato D., Solitary waves of the nonlinear Klein-Gordon field equation coupled with the Maxwell equations, Rev. Math. Phys. 14 (2002), 409–420.

    Article  MATH  Google Scholar 

  3. Benci V. Fortunato D., Solitary waves of the Semilinear Maxwell equations and their dynamical properties, in preparation.

    Google Scholar 

  4. Berestycki H., Lions P.L., Nonlinear Scalar Field Equations, I-Existence of a Ground State, Arch. Rat. Mech. Anal., 82(4) (1983), 313–345.

    MATH  Google Scholar 

  5. Berg J., LÖfstrÖm J., I nterpolation Spaces, Springer-Verlag, Berlin, Heidelberg, New York, (1976).

    Google Scholar 

  6. Born M., Théorie non-linéaire du champ électromagnetique, Ann. Inst. H. Poincaré, 1937.

    Google Scholar 

  7. Born M., Infeld L., Foundations of the new field theory, Nature, 132 (1933), 1004.

    Google Scholar 

  8. Born M., Infeld L., Foundations of the new field theory, Proc. R. Soc. Lon. A, 144 (1934), 425–451.

    Article  MATH  Google Scholar 

  9. Gelfand I.M., Fomin S.V., Calculus of Variations, Prentice-Hall, Englewood Cliffs, N.J. (1963).

    Google Scholar 

  10. Jackson J.D., Classical electrodynamics, John Wiley & Sons., New York, London, (1962).

    Google Scholar 

  11. Landau L., Lifchitz E., Théorie des Champs, Editions Mir, Moscou, (1970).

    Google Scholar 

  12. Thirring W., Classical Mathematical Physics, Springer, New York, Vienna, (1997).

    Google Scholar 

  13. Yang Y., Classical solutions in the Born-Infeld theory, Proc. R. Soc. Lon. A (2000), 456, 615–640.

    Article  MATH  Google Scholar 

  14. Yang Y., Solitons in Field Theory and and Nonlinear Analysis, Springer, New York, Berlin, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica Applicata “U. Dini”, Università degli Studi di Pisa, Via Bonanno 25/b, 56126, Pisa, Italy

    Vieri Benci

  2. Dipartimento di Matematica, Università di Bari, Via Orabona 4, 70125, Bari, Italy

    Donato Fortunato

Authors
  1. Vieri Benci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Donato Fortunato
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire Jacques-Louis Lions B.C. 187, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Thierry Cazenave

  2. Department of Mathematical Sciences, University of Nevada, Las Vegas, NV, 89154-4020, USA

    David Costa

  3. Instituto de Matemática, UNICAMP - IMECC, Caixa Postal: 6065, 13083-859, Campinas, SP, Brasil

    Orlando Lopes

  4. Departamento de Ingenieria Matemática Facultad de Ciencias Fisicas y Matemáticas, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile

    Raúl Manásevich

  5. Mathematics Department, University of Wisconsin-Madison, 480 Lincoln Dr, Madison, WI, 53706-1388, USA

    Paul Rabinowitz

  6. Dipartimento di Matematica, Università degli Studi, Via Saldini 50, 20133, Milano, Italy

    Bernhard Ruf

  7. Departamento de Matemática, PUC Rio, Rua Marquês de São Vicente, 225 EdifÍcio Cardeal Leme, Gávea - Rio de Janeiro, 22453-900, Brasil

    Carlos Tomei

Additional information

Dedicated to our friend Djairo

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Birkhäuser Verlag Basel/Switzerland

About this chapter

Cite this chapter

Benci, V., Fortunato, D. (2005). A Unitarian Approach to Classical Electrodynamics: The Semilinear Maxwell Equations. In: Cazenave, T., et al. Contributions to Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 66. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7401-2_3

Download citation

Publish with us

Policies and ethics

Search

Navigation