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We introduce low regularity exponential-type integrators for nonlinearSchr\"odinger equations for which first-order convergence only requires theboundedness of one additional derivative of the solution. More precisely, wewill prove first-order convergence in $H^r$ for solutions in $H^{r+1}$($r>d/2$) of the derived schemes. This allows us lower regularity assumptionson the data in the energy space than for instance required for classicalsplitting or exponential integration schemes. For one dimensional quadraticSchr\"odinger equations we can even prove first-order convergence without anyloss of regularity. Numerical experiments underline the favorable errorbehavior of the newly introduced exponential-type integrators for lowregularity solutions compared to classical splitting and exponentialintegration schemes.

Low regularity exponential-type integrators for semilinear Schr\"odinger equations