Standing waves for discrete Schrodinger equations in infinite lattices with saturable nonlinearities

被引：29

作者：

Chen, Guanwei ^{[1
]}

Ma, Shiwang ^{[2
,3
]}

Wang, Zhi-Qiang ^{[4
]}

机构：

[1] Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[4] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 261卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Discrete nonlinear Schrodinger equations; Saturable nonlinearities; Nontrivial solitons; Spectral gap; Spectral endpoint; GAP SOLITONS; EXISTENCE; BREATHERS; STABILITY;

D O I：

10.1016/j.jde.2016.05.030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the periodic discrete nonlinear equation [GRAPHICS] where L is a Jacobi operator, and the nonlinearities g(n)(s) are asymptotically linear as |s| -> infinity. In the two different cases (omega is a spectral endpoint of L, or it belongs to a finite spectral gap of L), we obtain the existence of nontrivial solitons of this equation by using variational methods. In particular, a necessary and sufficient condition is obtained for the existence of gap solitons of the nonlinear equation. Here, solitons appear when we look for standing waves of some discrete nonlinear Schrodinger equations. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：3493 / 3518

页数：26

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