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Non-linear secular-free solution of a model equation

  • G. C. Pramanik
Article
  • 13 Downloads

Abstract

The perturbation technique of Krylov—Bogoliubov—Mitropolsky is used to derive a secular-free solution up to third order of a model equation
$$C^2 \frac{{\partial ^2 \Phi }}{{\partial x^2 }} + \frac{{\partial ^2 \Phi }}{{\partial t^2 }} + \omega _0^2 \Phi + C^2 \Phi ^3 = 0$$
whereC and ω0 are constants in space and time. Expressions are obtained for amplitude dependent frequency shifts and wave number shifts.

Keywords

Model Equation Frequency Shift Order Approximation Monochromatic Wave Plasma Theory 
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.

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References

  1. 1.
    D. Montgomery andD. A. Tidman, Phys. fluids,7, 242, 1964.MATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    T. J. Boyd, Phys. fluids,10, 896, 1967.CrossRefADSGoogle Scholar
  3. 3.
    K. P. Das, Phys. fluids,11, 2055, 1968.CrossRefADSGoogle Scholar

Copyright information

© with the authors 1975

Authors and Affiliations

  • G. C. Pramanik
    • 1
  1. 1.Department of Mechanical EngineeringJadavpur UniversityCalcuttaIndia

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