Existence of dark solitons in discrete nonlinear Schrödinger equations with non-weak couplings

  • Kazuyuki YoshimuraEmail author
Original Paper


The anti-integrable limit for the discrete nonlinear Schrödinger equation is defined as the limit of vanishing couplings. There are an infinite number of trivial discrete dark solitons in this limit. The existence of discrete dark solitons continued from them has been proved only for sufficiently weak couplings. In the present paper, we focus on the case of non-weak couplings and prove the existence of discrete dark solitons over an explicitly given range of the coupling constant.


Discrete nonlinear Schrödinger equation Dark soliton 

Mathematics Subject Classification

37K60 37N20 35Q55 



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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringTottori UniversityTottoriJapan

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