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math.AP2022★ 2 cited
Global continua of solutions to the Lugiato-Lefever model for frequency combs obtained by two-mode pumping
Elias Gasmi, Tobias Jahnke, Michael Kirn +1
We consider Kerr frequency combs in a dual-pumped microresonator as time-periodic and spatially -periodic traveling wave solutions of a variant of the Lugiato-Lefever equation,…
math.AP2022
Approximation of high-frequency wave propagation in dispersive media
Julian Baumstark, Tobias Jahnke
We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter ,…
math.AP2022
Polarized high-frequency wave propagation beyond the nonlinear Schrödinger approximation
Julian Baumstark, Tobias Jahnke, Christian Lubich
This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations…