Journal of Physical Studies 5(2), 107–110 (2001) DOI: https://doi.org/10.30970/jps.05.107 ON THE THEORY OF THE NONLINEAR DISPERSION OF WAVE PACKETS IN THE MULTIPLE SCALES METHOD V. P. Lukomskii, Yu. V. Sedletskii Institute of Physics of the National Academy of Sciences of Ukraine 46 Nauky Pr., Kyiv, UA–03039, Ukraine

The time evolution of spectrally narrow wavetrain that is described by the nonlinear Klein-Gordon equation is investigated in weakly nonlinear medium. The asymptotic expansion of a solution is built by the method of multiple scales up to $ϵ ^5$ inclusive. This expansion is defined by a complex function that has the sense of the first harmonic of a solution which satisfies the nonlinear evolutionary Schrödinger equation of a higher order.

PACS number(s): 05.45.-a

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