Non-linear secular-free solution of a model equation

  • G. C. Pramanik


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.


Model Equation Frequency Shift Order Approximation Monochromatic Wave Plasma Theory 
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    T. J. Boyd, Phys. fluids,10, 896, 1967.CrossRefADSGoogle Scholar
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    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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