The Complex Modified Korteweg-de Vries Equation, a Non-Integrable Evolution Equation

  • Charles F. F. Karney
  • Abhijit Sen
  • Flora Y. F. Chu
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 8)


Some anisotropic media, e.g. a magnetized plasma, can support propagating electrostatic waves. We wish to study the dispersion and nonlinear self-modulation of such waves when the system is two-dimensional (x and y, x being the principal axis) and has reached a steady state [all field quantities ~ exp(- iωt), ω = constant]. We will take the medium to be homogeneous and non-dissipative, and will assume that the dielectric tensor depends on the electric field amplitude squared. The equation for the complex electric potential, ⌽ , is
$$\nabla \bullet \overline{\overline K} \left( {\nabla ,{{\left| {\nabla \phi } \right|}^2}} \right) \bullet \nabla \phi = 0$$


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  1. 1.
    C. F. F. Karney, A. Sen, F. Y. F. Chu: Plasma Physics Laboratory Report PPPL-1452, Princeton University (1978)Google Scholar
  2. 2.
    M. J. Ablowitz, D. J. Kaup, A. C. Newell, H. Segur: Stud. Appl. Math. 53, 249–315 (1974)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Charles F. F. Karney
    • 1
  • Abhijit Sen
    • 2
  • Flora Y. F. Chu
    • 3
  1. 1.Plasma Physics LaboratoryPrinceton UniversityPrincetonUSA
  2. 2.Plasma Fusion CenterMassachusetts Institute of Technology CambridgeUSA
  3. 3.Electronic Systems Laboratory and Department of Electrical Engineering and Computer ScienceMassachusetts Institute of Technology CambridgeUSA

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