The influence of linear damping on nonlinearly coupled positive and negative energy waves

Publisher Website
Google Scholar
Abstract
The linearly damped response to the nonlinear resonant mixing of two monochromatic coherent waves, involving modes of different energy sign, is shown to be always explosively unstable. Degeneration theory, modified to encompass explosively unstable solutions, is then applied to distinguish regions of negligible and strong damping, where the equations can be solved analytically. Effective damping, characterized by a damping rate ν, much higher than the (normalized) initial excitation U0, of the source waves, increases the explosion time by a factor of ν/U0.