Existence of discrete solitons in discrete nonlinear Schrödinger equations with non-weak couplings
- 138 Downloads
Discrete solitons are spatially localized periodic solutions in the discrete nonlinear Schrödinger equation. The anti-integrable limit is defined for the discrete nonlinear Schrödinger equation as the limit of vanishing couplings. There are an infinite number of trivial discrete solitons in this limit, each of which consists of a finite number of excited sites. The existence of discrete 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 solitons over an explicitly given range of the coupling constant.
KeywordsDiscrete nonlinear Schrödinger equation Discrete soliton
Mathematics Subject Classification37K60 37N20 35Q55
The author would like to thank M. Inubushi for his careful reading of the manuscript and helpful comments and the members of NTT Communication Science Laboratories for their continuous encouragement and support.
- 7.Yoshimura, K., Doi, Y., Kimura, M.: Localized modes in nonlinear discrete systems. In: Ohtsu, M., Yatsui, T. (eds.) Progress in Nanophotonics 3, pp. 119–166. Springer, New York (2014)Google Scholar
- 8.Eilbeck, J.C., Johansson, M.: The discrete nonlinear Schrödinger equation—20 years on. In: Vázquez, L., et al. (eds.) Localization and Energy Transfer in Nonlinear Systems, pp. 44–67. World Scientific, Singapore (2002)Google Scholar