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- W2058507017 abstract "The linearized coupled-mode equations for parametric instability are solved exactly for various cases. The exact evolution of a localized wave-pulse in an unbounded interaction region is used to illustrate the relationship between damping rates, group velocities and instability. Criteria for absolute and convective instability follows in a natural way. The pulse-evolution in a finite interaction region is presented. It is shown that the boundaries create kinks in the pulse-profile travelling back and forth at the group velocities, and that the over-all effect of finiteness is to reduce the instability growth. The instability development from a time-constant point source, turned on at a given time, is studied. We find that in the case of parallel group velocities, the solution is stationary behind a front moving with the slowest group velocity. When the group velocities are anti-parallel, and the criterion for convective instability is satisfied, the amplitudes grow asymptotically towards a stationary solution which is explicitly given. Finally, it is demonstrated that a mismatch in frequency or wave number will produce frequency and wave number shifts, but does not otherwise change the growth of the instability." @default.
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- W2058507017 date "1980-01-01" @default.
- W2058507017 modified "2023-09-25" @default.
- W2058507017 title "Space-Time Solutions of the Linearized Coupled-Mode Equations" @default.
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- W2058507017 doi "https://doi.org/10.1088/0031-8949/22/2/009" @default.
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