On existence of dark solitons in cubic-quintic nonlinear Schrödinger equation with a periodic potential

2006/06/05 by Pedro J. Torres, Torres, Pedro J., Vladimir V. Konotop +1
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Pattern Formation and Solitons (nlin.PS) #cond-mat.other #nlin.CD #nlin.PS

paper · pdf · doi:10.48550/arxiv.nlin/0606016

10 pages

arxiv created 2006/06/05 · arxiv updated 2009/12/01

Abstract

A proof of existence of stationary dark soliton solutions of the cubic-quintic nonlinear Schrödinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic on the Poincaré map.

Related

• On the existence of dark solitons of the cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity
• Dark solitons for an extended quintic nonlinear Schrödinger equation: Application to water waves at kh = 1.363
• Stationary localized modes in the quintic nonlinear Schrodinger equation with a periodic potential
• Periodic oscillations of dark solitons in parabolic potentials
• Bifurcating bright and dark solitary waves of the nearly nonlinear cubic-quintic Schrodinger equation