# Blow-up of solutions of nonlinear Schr\"odinger equations with oscillating nonlinearities

## TL;DR

This paper demonstrates finite time blow-up of solutions for 1-D nonlinear Schrödinger equations with oscillating nonlinearities in different domains, allowing non-negative initial energy and infinite momentum, using virial identities with weighted functions.

## Contribution

It extends blow-up results to cases with non-negative energy and infinite momentum by employing weighted virial identities, unlike previous studies.

## Key findings

- Solutions blow up in finite time under new conditions.
- The method applies to both interior and boundary nonlinearities.
- Numerical examples confirm the theoretical results.

## Abstract

The finite time blow-up of solutions for 1-D NLS with oscillating nonlinearities is shown in two domains: (1) the whole real line where the nonlinear source is acting in the interior of the domain and (2) the right half-line where the nonlinear source is placed at the boundary point. The distinctive feature of this work is that the the initial energy is allowed to be non-negative and the momentum is allowed to be infinite in contrast to the previous literature on the blow-up of solutions with time dependent nonlinearities. The common finite momentum assumption is removed by using a compactly supported or rapidly decaying weight function in virial identities - an idea borrowed from Ogawa-Tsutsumi (1991). At the end of the paper, a numerical example satisfying the theory is provided.