SELF-LOCALIZED SOLITON SOLUTIONS OF THE NONLINEAR QUANTUM HARMONIC OSCILLATOR


Bayindir C., Ozaydin F.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.12, no.2, pp.412-424, 2022 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2022
  • Title of Journal : TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Page Numbers: pp.412-424
  • Keywords: Nonlinear quantum harmonic oscillator, self-localized soliton stability, spectral renormalization method, split-step Fourier method, BRIGHT

Abstract

We analyze the existences, properties and stabilities of the self-localized solutions of the nonlinear quantum harmonic oscillator (NQHO) using spectral renormalization method (SRM). We show that self-localized single and dual soliton solutions of the NQHO do exist. Additionally we report that single and dual soliton solutions satisfy the necessary Vakhitov and Kolokolov slope condition, at least for the parameter ranges considered. Additionally, we investigate the stability characteristics of the single and dual soliton solutions using a split-step Fourier scheme. We show that single and dual soliton solutions are pulsating during time stepping. We discuss our findings and comment on our results.