Anomalous autoresonance threshold for chirped-driven Korteweg-de-Vries waves

L. Friedland, A. G. Shagalov, S. V. Batalov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Large amplitude traveling waves of the Korteweg-de-Vries (KdV) equation can be excited and controlled by a chirped frequency driving perturbation. The process involves capturing the wave into autoresonance (a continuous nonlinear synchronization) with the drive by passage through the linear resonance in the problem. The transition to autoresonance has a sharp threshold on the driving amplitude. In all previously studied autoresonant problems the threshold was found via a weakly nonlinear theory and scaled as α3/4,α being the driving frequency chirp rate. It is shown that this scaling is violated in a long wavelength KdV limit because of the increased role of the nonlinearity in the problem. A fully nonlinear theory describing the phenomenon and applicable to all wavelengths is developed.

Original languageEnglish
Article number042924
JournalPhysical Review E
Volume92
Issue number4
DOIs
StatePublished - 28 Oct 2015

Bibliographical note

Publisher Copyright:
© 2015 American Physical Society.

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