3 papers
math.NA2025
The Fourier spectral approach to the spatial discretization of quasilinear hyperbolic systems
Vincent Duchêne, Johanna Ulvedal Marstrander
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability…
math.AP2024
Remarks on solitary waves in equations with nonlocal cubic terms
Johanna Ulvedal Marstrander
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x…
math.AP2023
Solitary waves for dispersive equations with Coifman-Meyer nonlinearities
Johanna Ulvedal Marstrander
Using a modified version of Weinstein's argument for constrained minimization in nonlinear dispersive equations, we prove existence of solitary waves in fully nonlocally nonlinear…