Existence of multi-solitons for logarithmic Schr{ö}dinger equation with a perturbation of a smooth $L^2$-subcritical function nonlinearity
Year: 2026
Type: preprint
Abstract: In this paper, we study the nonlinear Schr{ö}dinger equation with a nonlinearity combining a focusing logarithmic term and a smooth $L^2$-subcritical function. Our main result is the construction of multisoliton solutions for this equation. These special configurations behave asymptotically, for large times, as the superposition of several solitons moving with distinct velocities. The proof relies on an iterative construction method combined with localized energy estimates adapted to the mixed structure of the nonlinearity.
Source: arXiv (Cornell University)
Author: Bensaid, Mohamed
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Université de Lille
Award: G5016747878
OpenAlex ID: W7213497484