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arXiv · 2503.17808

Multi-phase autoresonant excitations in the Korteweg-de-Vries system

L. Friedland·A. G. Shagalov
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Abstract

Autoresonant (continuously phase-locked) two-phase waves of the Korteweg-de-Vries equation are excited and controlled using a two-component, small amplitude, chirped frequency driving. These solutions are analyzed in the weakly nonlinear regime. The theory is based on Whitham's averaged variational principle. The problem is reduced to a fully separated two degrees of freedom dynamical problem. This separation allows for simple derivation of the autoresonant thresholds on the driving wave amplitudes. We also excite more complex 4-phase autoresonant waves. The inverse scattering analysis of this case indicates again the separation of all four degrees of freedom in the associated weakly nonlinear dynamical problem.

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L. Friedland, A. G. Shagalov. 2025-03-22. Multi-phase autoresonant excitations in the Korteweg-de-Vries system. https://arxiv.org/abs/2503.17808

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