Blow-up criteria for the 1D NLS with combined nonlinearities
Analysis of PDEs
2026-02-25 v1
Abstract
In this paper we develop two different types of criteria for the finite time blow-up solutions to the combined nonlinear Schr\"odinger equation in 1D. The first one is a negative energy criterion developed for triple combined nonlinearity and then for a (convergent) infinite sum of combined nonlinearities, including an exponential nonlinearity. The second one is a positive energy criterion for the double nonlinearity with the defocusing-focusing coefficients. We also provide examples of initial data that satisfy either of the criteria.
Keywords
Cite
@article{arxiv.2602.21040,
title = {Blow-up criteria for the 1D NLS with combined nonlinearities},
author = {Alex D Rodriguez},
journal= {arXiv preprint arXiv:2602.21040},
year = {2026}
}
Comments
29 pages