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math.AP2025
Global existence and decay of small solutions in a viscous half Klein-Gordon equation
Louis Garénaux, Björn de Rijk
We establish global existence and decay of solutions of a viscous half Klein-Gordon equation with a quadratic nonlinearity considering initial data, whose Fourier transform is smal…
math.AP2025
Orbital stability of plane waves in the Klein-Gordon equation against localized perturbations
Emile Bukieda, Louis Garénaux, Björn de Rijk
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render…
math.AP2025
Existence and stability of soliton-based frequency combs in the Lugiato-Lefever equation
Lukas Bengel, Björn de Rijk
Kerr frequency combs are optical signals consisting of a multitude of equally spaced excited modes in frequency space. They are generated by converting a continuous-wave pump laser…