PreprintCC BY 4.0HAL
INFINITE CASCADES FOR THE CUBIC NONLINEAR HALF-WAVE EQUATION ON THE LINE
Abstract
We construct infinite-time Sobolev cascades for the cubic nonlinear half-wave equation on the real line. For 1/2<s≤1 and 0≤κ<2s(2s−1)/(4s−1), spatial gluing of permanently saturated two-soliton packets gives a dense set of strictly mass-subthreshold data for which |u(t)|Hs/(1+t)κ→∞ in the focusing case. A second construction replicates finite-burst Szegő packets without rescaling. It yields a dense Gδ subset of H∞(ℝ) whose solutions perform logarithmic cascades in every Hs with s>1/2 in the focusing case and in the defocusing case.
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BibTeX
@misc{chen2026infinite,
title = {{INFINITE CASCADES FOR THE CUBIC NONLINEAR HALF-WAVE EQUATION ON THE LINE}},
author = {Xi Chen},
howpublished = {HAL},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2609.27813},
eprint = {2609.27813},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05731979v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - INFINITE CASCADES FOR THE CUBIC NONLINEAR HALF-WAVE EQUATION ON THE LINE
AU - Xi Chen
PY - 2026
DA - 2026/08/31
PB - HAL
DO - 10.48550/arxiv.2609.27813
UR - https://hal.science/hal-05731979v1
AB - We construct infinite-time Sobolev cascades for the cubic nonlinear half-wave equation on the real line. For 1/2<s≤1 and 0≤κ<2s(2s−1)/(4s−1), spatial gluing of permanently saturated two-soliton packets gives a dense set of strictly mass-subthreshold data for which |u(t)|_H^s/(1+t)^κ→∞ in the focusing case. A second construction replicates finite-burst Szegő packets without rescaling. It yields a dense G_δ subset of H^∞(ℝ) whose solutions perform logarithmic cascades in every H^s with s>1/2 in the focusing case and in the defocusing case.
ER -