Modulational instability and gap solitons in a finite Josephson transmission line
- Laboratoire Ondes et Structures Coherentes (OSC), Faculte des Sciences et Techniques, Universite de Bourgogne, 6 Boulevard Gabriel, 21100 Dijon, France (FR)
We concentrate on the modulational instability that may develop and perturb the gap soliton or nonlinear standing wave that appears in a finite Josephson transmission line (Phys. Rev. B 41, 10387 (1990)) when it has switched to a transmitting state. We first calculate theoretically the spatial dependence of the gap-soliton envelope or nonlinear standing wave inside the system, in terms of Jacobi elliptic functions. Our results fit reasonably well the envelope measured via our computer experiments on the dynamics of the system. Approaching the standing-wave structure in terms of two counterpropagating waves, we show that the evolution of their slowly varying amplitudes can be modeled by two coupled nonlinear Schroedinger equations. Then we calculate the critical wave number and growth rate of the instability for the two counter waves, which is three times larger than the growth rate of either wave alone. The corresponding critical temporal frequency, at which the modulational instability may appear, is in good agreement with the value determined from our numerical experiments.
- OSTI ID:
- 5633978
- Journal Information:
- Physical Review, B: Condensed Matter; (USA), Vol. 43:9; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
JOSEPHSON JUNCTIONS
SOLITONS
CRITICAL FREQUENCY
ENERGY GAP
INSTABILITY GROWTH RATES
NONLINEAR OPTICS
SINE-GORDON EQUATION
WAVE PROPAGATION
EQUATIONS
FIELD EQUATIONS
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OPTICS
QUASI PARTICLES
SUPERCONDUCTING JUNCTIONS
426001* - Engineering- Superconducting Devices & Circuits- (1990-)