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Dissipative bright and dark pulses under periodic forcing
Lukas Bengel, Björn de Rijk
We analyze the existence and stability of bright and dark pulses in a damped nonlinear Schrödinger (NLS) equation with periodic forcing. This Lugiato-Lefever equation is a canonica…
Dynamics of dissipative periodic optical waves in an external potential
Lukas Bengel
We study the dynamics of periodic waves in a damped-driven nonlinear Schrödinger (NLS) equation perturbed by a small spatially dependent transport term. This equation arises in non…
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…
Multiple front and pulse solutions in spatially periodic systems
Lukas Bengel, Björn de Rijk
In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semi…
Stability of solitary wave solutions in the Lugiato-Lefever equation
Lukas Bengel
We analyze the spectral and dynamical stability of solitary wave solutions to the Lugiato-Lefever equation (LLE) on . Our interest lies in solutions that arise through…
Pinning in the extended Lugiato-Lefever equation
Lukas Bengel, Dmitry Pelinovsky, Wolfgang Reichel
We consider a variant of the Lugiato-Lefever equation (LLE), which is a nonlinear Schrödinger equation on a one-dimensional torus with forcing and damping, to which we add a first-…