Publications
Journal Articles
Mazzucchi, Sonia; Nicola, Fabio; Trapasso, S. Ivan
Phase space analysis of higher-order dispersive equations with point interactions Journal Article
In: Comm. Partial Differential Equations, vol. 51, iss. 5, pp. 564–584, 2026.
Abstract | Links | BibTeX | Tags: dispersive equations, modulation spaces, partial differential equations, point interactions
@article{MNT_hodisp_24,
title = {Phase space analysis of higher-order dispersive equations with point interactions},
author = {Sonia Mazzucchi and Fabio Nicola and S. Ivan Trapasso},
url = {https://arxiv.org/abs/2407.15521, arXiv
https://www.tandfonline.com/doi/epdf/10.1080/03605302.2026.2702344?needAccess=true, PDF},
doi = {10.1080/03605302.2026.2702344},
year = {2026},
date = {2026-06-23},
urldate = {2026-06-23},
journal = {Comm. Partial Differential Equations},
volume = {51},
issue = {5},
pages = {564–584},
abstract = {We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave packets) of the corresponding fundamental solution - in fact, locating the modulation/amalgam space regularity of such generalized Fresnel-type oscillatory functions is a problem of independent interest in harmonic analysis.},
keywords = {dispersive equations, modulation spaces, partial differential equations, point interactions},
pubstate = {published},
tppubtype = {article}
}
We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave packets) of the corresponding fundamental solution – in fact, locating the modulation/amalgam space regularity of such generalized Fresnel-type oscillatory functions is a problem of independent interest in harmonic analysis.