Advertisement

The Lagrangian Approach to Nonlinear Wave Propagation

  • J. M. Arnold
Part of the NATO ASI Series book series (NSSB, volume 247)

Abstract

The increasing importance of nonlinear phenomena in optics makes it essential that a theoretical framework should be developed having sufficient generality to encompass the full range of nonlinear phenomena under investigation, yet which is sufficently flexible to enable analytical calculation of the basic phenomena to be realistic. Nonlinear optics, by definition, involves nonlinear partial differential equations. In particular, Maxwell’s equations are coupled to a Schrödinger equation via a nonlinear polarisation. The wide range of Hamiltonians which can appear in the Schrödinger equation dictates the generality required of the theoretical methods.

Keywords

Trial Function Nonlinear Partial Differential Equation SchrOdinger Equation Nonlinear SchrOdinger Equation Nonlinear Wave Propagation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. B. Whitham, Linear and nonlinear waves (Academic, 1974).Google Scholar
  2. 2.
    T. Kawahara, Plasma Phys. 18, 305–316 (1977).ADSCrossRefGoogle Scholar
  3. 3.
    R. Bullough, P. M. Jack, P. W. Kitchenside and R. Saunders, Phys. Scr. 20, 364–381 (1979).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    P. M. Jack, Ph.D. thesis, UMIST.Google Scholar
  5. 5.
    D. Anderson, Phys. Rev. A 27, 3135–3145 (1983).ADSCrossRefGoogle Scholar
  6. 6.
    D. Anderson and M. Lisak, Phys. Rev. A 27, 1393–1398 (1983).ADSCrossRefGoogle Scholar
  7. 7.
    A. Bondeson, D. Anderson and M. Lisak, Phys. Scr. 20, 479 (1979).MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and nonlinear wave equations (Academic, 1982).Google Scholar
  9. 9.
    A. C. Newell, Solitons in mathematics and physics (SIAM, Philadelphia, 1985).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • J. M. Arnold
    • 1
  1. 1.Department of Electronics and Electrical EngineeringUniversity of GlasgowGlasgowScotland

Personalised recommendations