Asymptotic behavior of solutions to nonlinear Schr\"{o}dinger equations with time-dependent harmonic potentials

TL;DR

This paper investigates how solutions to nonlinear Schrödinger equations with time-dependent harmonic potentials behave asymptotically, demonstrating their decay over time especially under long-range nonlinearities.

Contribution

It establishes the time-decay properties of solutions with long-range power nonlinearities in the context of time-dependent harmonic oscillators.

Findings

Solutions exhibit decay over time under specified conditions.

Decay rates depend on the nonlinearity's power type.

Results extend understanding of long-range nonlinear Schrödinger equations.

Abstract

In this study, we examine the asymptotic behavior of solutions to nonlinear Schr\"{o}dinger equations with time-dependent harmonic oscillators and prove the time-decay property of solutions in the case of a long range power type nonlinearity.