International Journal of Theoretical Physics

, Volume 35, Issue 12, pp 2489–2499 | Cite as

Solitary waves interacting with an external field

  • T. G. Bodurov


It is shown that the equations of a solitary wave interacting with an external field can be obtained from the noninteraction equations and a substitution analogous to the prescription of quantum mechanics for the energy and momentum operators in the presence of an interaction. Next it is shown that, if the rate of change of the external field is sufficiently small, then the motion of the solitary wave as a whole is identical to that of a point charge in an electromagnetic field or to that of a point mass in a given interaction potential. This identity holds regardless of the specific solitary wave equation. An estimate for the external field maximal rate of change is derived.


Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic Wave Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, D. (1971). Stability of time-dependent particlelike solutions in nonlinear field theories II,Journal of Mathematical Physics,12, 945–952.Google Scholar
  2. Anderson, D., and Derrick, G. (1970). Stability of time-dependent particlelike solutions in nonlinear field theories I,Journal of Mathematical Physics,11, 1336–1346.Google Scholar
  3. Berger, M. (1972). On the existence and structure of stationary states for a nonlinear KG equation,Journal of Functional Analysis,9, 249–261.Google Scholar
  4. Cooperstock, F., and Rosen, N. (1989). A nonlinear gauge-invariant field theory of leptons,International Journal of Theoretical Physics,28, 423–440.Google Scholar
  5. Deumens, E. (1986). The Klein-Gordon-Maxwell system of equations,Physica D,18, 371–373.Google Scholar
  6. Friedberg, R., Lee, T. D., and Sirlin, A. (1976). Class of scalar-field soliton solutions in three space dimensions,Physical Review D,13, 2739–2761.Google Scholar
  7. Goldstein, H. (1981).Classical Mechanics, 2nd ed., Addison-Wesley, Reading, Massachusetts.Google Scholar
  8. Grillakis, J., Shatah, J., and Strauss, W. (1987). Stability theory of solitary waves in the presence of symmetry,Journal of Functional Analysis,74, 160–197.Google Scholar
  9. Jackson, J. (1975).Classical Electrodynamics, 2nd ed., Wiley, New York.Google Scholar
  10. Kobushkin, A., and Chepilko, N. (1990). Soliton model of elementary electrical charge,Matematicheskaia Fizika,83(3), 349–359 [in Russian].Google Scholar
  11. Kramers, H. (1958).Quantum Mechanics, North-Holland, Amsterdam.Google Scholar
  12. Lee, T. D. (1981).Particle Physics and Introduction to Field Theory, Harwood.Google Scholar
  13. Logan, J. (1977).Invariant Variational Principles, Academic Press, New York.Google Scholar
  14. Okolowski, J., and Slomiana, M. (1988). Particlelike solutions to nonlinear classical real field theories,Journal of Mathematical Physics. 29, 1837–1839.Google Scholar
  15. Rosen, N. (1939). A field theory of elementary particles,Physical Review,55, 94–101.Google Scholar
  16. Strauss, W. (1989).Nonlinear Wave Equations, AMS, Providence, Rhode Island.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • T. G. Bodurov
    • 1
  1. 1.Eugene

Personalised recommendations