Excitation of solitons by an external resonant wave with a slowly varying phase velocity

Igor Aranson, Baruch Meerson, Toshiki Tajima

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A mechanism is proposed for the excitation of solitons in nonlinear dispersive media. The mechanism employs an external pumping wave with a varying phase velocity, which provides a continuous resonant excitation of a nonlinear wave in the medium. Two different schemes of a continuous resonant growth (continuous phase locking) of the induced nonlinear wave are suggested. The first of them requires a definite time dependence of the pumping-wave phase velocity and is relatively sensitive to the initial wave phase. The second employs the dynamic autoresonance effect and is insensitive to the exact time dependence of the pumping-wave phase velocity. It is demonstrated analytically and numerically, for a particular example of a driven Kortewegde Vries (KdV) equation with periodic boundary conditions, that as the nonlinear wave grows, it transforms into a soliton, which continues growing and accelerating adiabatically. A fully nonlinear perturbation theory is developed for the driven KdV equation to follow the growing wave into the strongly nonlinear regime and describe the soliton formation.

Original languageEnglish (US)
Pages (from-to)7500-7510
Number of pages11
JournalPhysical Review A
Issue number10
StatePublished - 1992

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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