Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation
Analysis of PDEs
2026-01-13 v2
Abstract
This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show that near a characteristic blow-up point, the solution behaves exactly as in the real-valued case. Namely, up to a rotation in the complex plane, the solution decomposes into a sum of a finite number of decoupled solitons with alternate signs. The main novelty of our proof is a resolution of a complex-valued first order Toda system governing the evolution of the positions and the phases of the solitons.
Keywords
Cite
@article{arxiv.2501.04505,
title = {Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation},
author = {Asma Azaiez and Jacek Jendrej and Hatem Zaag},
journal= {arXiv preprint arXiv:2501.04505},
year = {2026}
}
Comments
48 pages, 2 figures