Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2026

Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation

Asma Azaiez
  • Fonction : Auteur
Jacek Jendrej
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-04881422 , version 1 (12-01-2025)

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Asma Azaiez, Jacek Jendrej, Hatem Zaag. Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation. Proceedings of the London Mathematical Society, In press. ⟨hal-04881422⟩
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