Stability of the higher-order splitting methods for the nonlinear Schrödinger equation with an arbitrary dispersion operator
DOI: https://doi.org/10.3846/mma.2024.20905Abstract
The numerical solution of the generalized nonlinear Schrödinger equation by simple splitting methods can be disturbed by so-called spurious instabilities. We analyze these numerical instabilities for an arbitrary splitting method and apply our results to several well-known higher-order splittings. We find that the spurious instabilities can be suppressed to a large extent. However, they never disappear completely if one keeps the integration step above a certain limit and applies what is considered to be a more accurate higher-order method. The latter can be used to make calculations more accurate with the same numerically stable step, but not to make calculations faster with a much larger step.
Keywords:
nonlinear optics, nonlinear fibers, nonlinear Schrödinger equation, generalized nonlinear Schrödinger equation (GNLSE), modulation instability (MI), four-wave mixing, spurious instabilities, splitting methodsHow to Cite
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