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

Abstract

In this paper we develop two different types of criteria for the finite time blow-up solutions to the combined nonlinear Schrödinger 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.

32 pages, published version at Studies in Applied Mathematics