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

Journal Article · Fri May 15 04:00:00 EDT 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.45.7500· OSTI ID:7105140

Aranson, I; Meerson, B ^[1]; Tajima, T ^[2]

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1. Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2. Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States) Department of Physics, The University of Texas at Austin, Austin, Texas 78712 (United States)

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 Korteweg--de 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.

• DOE Contract Number: FG05-80ET53088
• OSTI ID: 7105140
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 45:10; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700340* -- Plasma Waves
Oscillations
& Instabilities-- (1992-)
DIFFERENTIAL EQUATIONS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EXCITATION
FLUID MECHANICS
HYDRODYNAMICS
KORTEWEG-DE VRIES EQUATION
MECHANICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
PHASE VELOCITY
PLASMA WAVES
QUASI PARTICLES
SOLITONS
VELOCITY