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.