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arXiv · 2602.21040

Blow-up criteria for the 1D NLS with combined nonlinearities

Alex D Rodriguez
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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.

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Alex D Rodriguez. 2026-02-24. Blow-up criteria for the 1D NLS with combined nonlinearities. https://doi.org/10.1111/sapm.70272

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