title: Anomalous autoresonance threshold for chirped-driven Korteweg-de-Vries waves.
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 α(3/4),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.
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: L
authors.initials: L
authors.lastname: Friedland
authors.affiliation: Institute of Metal Physics, Ekaterinburg 620990, Russian Federation and Ural Federal University, Mira 19, Ekaterinburg 620002, Russian Federation.
authors.forename: A G
authors.initials: AG
authors.lastname: Shagalov
authors.affiliation: Institute of Metal Physics, Ekaterinburg 620990, Russian Federation and Ural Federal University, Mira 19, Ekaterinburg 620002, Russian Federation.
authors.forename: S V
authors.initials: SV
authors.lastname: Batalov