Dark solitons for an extended quintic nonlinear Schrödinger equation: Application to water waves at kh = 1.363

2018/10/30 by F. Tsitoura, Tsitoura, F., Theodoros P. Horikis +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.1810.12500

openalex publication_date 2018/10/30 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

We study the existence, formation and dynamics of gray solitons for an extended quintic nonlinear Schrödinger (NLS) equation. The considered model finds applications to water waves, when the characteristic parameter kh - where k is the wavenumber and h is the undistorted water's depth - takes the critical value kh=1.363. It is shown that this model admits approximate dark soliton solutions emerging from an effective Korteweg-de Vries equation and that two types of gray solitons exist: fast and slow, with the latter being almost stationary objects. Analytical results are corroborated by direct numerical simulations.

Related

• On existence of dark solitons in cubic-quintic nonlinear Schrödinger equation with a periodic potential
• Optical Nonlinear Dark X-Waves
• A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation: II. Dark soliton solutions
• Universal reductions and solitary waves of weakly nonlocal defocusing nonlinear Schrödinger equations
• On the existence of dark solitons of the cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity