Tripole-mode and quadrupole-mode solitons in (1\u2009+\u20091)-dimensional nonlinear media with a spatial exponential-decay nonlocality

Zhiping Dai,Xiaohui Ling,Shumin Zhang,Xingliang Li,Zhenjun Yang,Zhaoguang Pang,Youwen Wang

doi:10.1038/s41598-017-00197-6

Zhiping Dai, Xiaohui Ling + Show 5 more

Open Access

https://doi.org/10.1038/s41598-017-00197-6

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Abstract

The approximate analytical expressions of tripole-mode and quadrupole-mode solitons in (1 + 1)-dimensional nematic liquid crystals are obtained by applying the variational approach. It is found that the soliton powers for the two types of solitons are not equal with the same parameters, which is much different from their counterparts in the Snyder-Mitchell model (an ideal and typical strongly nolocal nonlinear model). The numerical simulations show that for the strongly nonlocal case, by expanding the response function to the second order, the approximate soliton solutions are in good agreement with the numerical results. Furthermore, by expanding the respond function to the higher orders, the accuracy and the validity range of the approximate soliton solutions increase. If the response function is expanded to the tenth order, the approximate solutions are still valid for the general nonlocal case.

Highlights

The nonlocal nonlinearity exsits naturally in many physical systems, such as nematic liquid crystals (NLCs)1–4, lead glasses5, atomic vapors6, Bose-Einstein condensates7, and photorefractive crystals8
Since a surface soliton in nonlocal nonlinear media can be regarded as a half of a bulk soliton with an antisymmetric amplitude distribution43, 44, the results on quadrupole-mode solitons here may be helpful for the investigation of the surface dipole nonlocal solitons
Let us roughly recall the derivation of the dimensionless nonlinear Schrödinger equation (NNLSE) for the (1 + 1)-dimensional NLCs based on refs 1, 31 and 45

Summary

Introduction

The nonlocal nonlinearity exsits naturally in many physical systems, such as nematic liquid crystals (NLCs)1–4, lead glasses5, atomic vapors6, Bose-Einstein condensates7, and photorefractive crystals8. In this paper, based on the variational approach, we study the tripole-mode and quadrupole-mode solitons in nonlinear media with an exponential-decay nonlocal response. If wm is fixed, the degree of nonlocality decreases with the increase of the soliton width, so the validity of approximate results is getting declined continuously [see Fig. 2(b)].

Results

Conclusion