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Unusual ways of four-wave mixing instability
2022, Amiranashvili, Shalva, Bandelow, Uwe
A pump carrier wave in a dispersive system may decay by giving birth to blue- and red-shifted satellite waves due to modulation or four-wave mixing instability. We analyse situations where the satellites are so different from the carrier wave, that the red-shifted satellite either changes its propagation direction (k < 0, ω > 0) or even gets a negative frequency (k, ω < 0). Both situations are beyond the envelope approach and require application of Maxwell equations.
Additive splitting methods for parallel solution of evolution problems
2020, Amiranashvili, Shalva, Radziunas, Mindaugas, Bandelow, Uwe, Busch, Kurt, Čiegis, Raimondas
We demonstrate how a multiplicative splitting method of order P can be used to construct an additive splitting method of order P + 3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourth-order additive method, which is yielded by the Lie-Trotter splitting. We provide error estimates, stability analysis, and numerical examples with the special discussion of the parallelization properties and applications to nonlinear optics.