7 papers · 1 filter
Explicit Fourier Integrator for the Periodic dNLS via Gauge Transformation: Low-Regularity Estimates in Discrete Bourgain Spaces
Lun Ji, Hang Li, Alexander Ostermann +1
The derivative nonlinear Schrödinger equation is a fundamental model for the propagation of nonlinear dispersive waves in, for example, plasma physics and nonlinear optics. In this…
A low regularity exponential-type integrator for the derivative nonlinear Schrödinger equation
Lun Ji, Hang Li, Alexander Ostermann
In this work, we present a first-order unfiltered exponential integrator for the one-dimensional derivative nonlinear Schrödinger equation with low regularity. Our analysis shows t…
Low-regularity error estimates of a filtered Lie-Trotter splitting scheme for the Zakharov system in arbitrary dimensions
Lun Ji, Hang Li, Chunmei Su
In this paper, we establish error estimates for a fully discrete, filtered Lie splitting scheme applied directly to the Zakharov system -- a model whose solutions may exhibit extre…
Error estimates of time-splitting schemes for nonlinear Klein--Gordon equation with rough data
Lun Ji, Xiaofei Zhao
In this work, we consider the convergence analysis of time-splitting schemes for the nonlinear Klein--Gordon/wave equation under rough initial data. The optimal error bounds of the…
Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates
Lun Ji, Hang Li, Alexander Ostermann +1
We investigate a filtered Lie-Trotter splitting scheme for the ``good" Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use o…
Low regularity error estimates for high dimensional nonlinear Schrödinger equations
Lun Ji, Alexander Ostermann
The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schrödinger equation at low regularity. Its temporal convergence…