On the existence of dark solitons of the cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity

2014/12/28 by Christos Sourdis, Sourdis, Christos
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.1412.8165

arxiv created 2014/12/28 · openalex publication_date 2014/12/28 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a simple proof of the existence of dark solitons of the defocusing cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity. Moreover, our proof allows for a broader class of inhomogeneities and gives some new properties of the solutions. We also apply our approach to the defocusing cubic-quintic nonlinear Schrodinger equation with a periodic potential.

Related

• On existence of dark solitons in cubic-quintic nonlinear Schrödinger equation with a periodic potential
• Dark solitons for an extended quintic nonlinear Schrödinger equation: Application to water waves at kh = 1.363
• Resonating the Schrödinger equation with cubic-quintic-septic-nonic and quadrupled power-law nonlinearities: Analytical analysis and discussion
• Connected and disconnected stable regions of solitons of nonlinear Schrödinger equation with PT-symmetric potential
• General N‐Dark–Dark Solitons in the Coupled Nonlinear Schrödinger Equations