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We demonstrate the new specific phenomenon of the long-time resonant energyexchange in the carbon nanotubes (CNTs) with the radial breathing mode as acarrier. This process turns out to be stable in the wide range of theexcitation energy. It is shown that the modified nonlinear Schr\"odingerequation, obtained in the framework of nonlinear elastic thin shell theory,describes the CNT nonlinear dynamics in the considered frequency band. Thenumerical integration of the thin shell theory equations confirms the resultsof the analytical study.

The radial breathing mode in CNT - the nonlinear theory of the resonant energy exchange