Resonances in Multifrequency Averaging Theory

  • S. Yu. Dobrokhotov
Part of the NATO ASI Series book series (NSSB, volume 320)


The Whitham method allows to obtain rapidly oscillating asymptotic solutions of nonlinear equations with a small parameter ε which characterizes the dispersion. The principal term of such asymptotic solutions can be represented in the form
$$ u = f\left( {\frac{{S\left( {x,t} \right)}}{\varepsilon },x,t} \right)$$
, where f (τ, x, t) and S(x, t) are smooth functions and f is 2π-periodic in the argument τ. The function (1.1) describes the distribution of wave packets. Such solutions were used in different physical and mechanical problems (see, for examplc, the bibliography in [1-16); they satisfy the special Cauchy data
$$ u{{|}_{{t = 0}}} = f\left( {\frac{{{{S}^{0}}\left( x \right)}}{\varepsilon },x,0} \right)$$


Wave Packet Asymptotic Solution Principal Term Adjoint Function Resonance Correction 
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© Springer Science+Business Media New York 1994

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  • S. Yu. Dobrokhotov

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