Nonlinear dynamics of periodic Lugiato-Lefever waves against sums of co-periodic and localized perturbations

Joannis Alexopoulos

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arXiv · 2504.20880

Nonlinear dynamics of periodic Lugiato-Lefever waves against sums of co-periodic and localized perturbations

Joannis Alexopoulos

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Abstract

In recent years, essential progress has been made in the nonlinear stability analysis of periodic Lugiato-Lefever waves against co-periodic and localized perturbations. Inspired by considerations from fiber optics, we introduce a novel iteration scheme which allows to perturb against sums of co-periodic and localized functions. This unifies previous stability theories in a natural manner.

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Joannis Alexopoulos. 2025-04-29. Nonlinear dynamics of periodic Lugiato-Lefever waves against sums of co-periodic and localized perturbations. https://arxiv.org/abs/2504.20880

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