Strong instability of standing waves for nonlinear Schr\"odinger equations with double power nonlinearity

TL;DR

This paper proves that certain standing wave solutions to nonlinear Schrödinger equations with double power nonlinearities are strongly unstable, leading to blowup behavior.

Contribution

It establishes the strong instability of standing waves in nonlinear Schrödinger equations with double power nonlinearities, a novel result in this context.

Findings

Standing waves are strongly unstable under certain conditions.

Instability leads to blowup of solutions.

Results contribute to understanding wave stability in nonlinear Schrödinger equations.

Abstract

We prove strong instability (instability by blowup) of standing waves for some nonlinear Schr\"odinger equations with double power nonlinearity.