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math.NA2026
A vanishing-viscosity minimizing movement Fourier spectral method for scalar conservation laws
Lun Ji, Buyang Li, Fangyan Yao
We propose a vanishing-viscosity minimizing movement (VVMM) Fourier spectral method for scalar hyperbolic conservation laws under periodic boundary conditions. The method is a full…
math.NA2026
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…
math.NA2026
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…