Linear modulational and subharmonic dynamics of spectrally stable Lugiato-Lefever periodic waves

We study the linear dynamics of spectrally stable T -periodic stationary solutions Lugiato-Lefever equation (LLE), a damped nonlinear Schrödinger with forcing that arises in optics. Such are nonlinearly to NT -periodic, i.e. subharmonic, perturbations for each N ∈ exponential decay rates form e − δ t . However, both and allowable size initial tend 0 as → ∞ , so this result is non-uniform and, fact, empty limit = The primary goal paper introduce methodology, context LLE, by which uniform stability subharmonic may be achieved, at least level. obtained shown agree precisely polynomial localized, integrable on real line, such periodic LLE. This work unifies expands several existing works literature concerning waves, sets forth general methodology studying problems other contexts.