On the existence of gap solitons in a periodic discrete nonlinear Schrodinger equation with saturable nonlinearity

被引：61

作者：

Zhou, Zhan ^{[1
]}

Yu, Jianshe ^{[1
]}

Chen, Yuming ^{[2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

来源：

NONLINEARITY | 2010年 / 23卷 / 07期

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

GUIDED-WAVES; BREATHERS; LATTICES; SYSTEMS; PROPAGATION; PROOF; MEDIA;

D O I：

10.1088/0951-7715/23/7/011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a periodic discrete nonlinear Schrodinger equation with saturable nonlinearity is considered. Using the critical point theory in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of gap solitons. Our results not only solve an open problem proposed by Pankov (2006 Nonlinearity 19 27-40) but also considerably improve some existing ones even for some special cases.

引用

页码：1727 / 1740

页数：14

共 28 条

[21] Periodic and decaying solutions in discrete nonlinear Schrodinger with saturable nonlinearity [J].

Pankov, Alexander ;

Rothos, Vassilis .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2008, 464 (2100) :3219-3236

[22]

Rabinowitz PH, 1986, MINIMAX METHODS CRIT

[23] Gap Solitons in Periodic Discrete Schrodinger Equations with Nonlinearity [J].

Shi, Haiping .

ACTA APPLICANDAE MATHEMATICAE, 2010, 109 (03) :1065-1075

[24] NONLINEAR THIN-FILM GUIDED-WAVES IN NON-KERR MEDIA [J].

STEGEMAN, GI ;

ARIYASU, J ;

SEATON, CT ;

SHEN, TP ;

MOLONEY, JV .

APPLIED PHYSICS LETTERS, 1985, 47 (12) :1254-1256

[25] GUIDANCE PROPERTIES OF NONLINEAR PLANAR WAVE-GUIDES [J].

STUART, CA .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1993, 125 (02) :145-200

[26] Envelope solution profiles of the discrete nonlinear Schrodinger equation with a saturable nonlinearity [J].

Yan, Zhenya .

APPLIED MATHEMATICS LETTERS, 2009, 22 (04) :448-452

[27] Breather solutions of the discrete nonlinear Schrodinger equations with unbounded potentials [J].

Zhang, Guoping .

JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (01)

[28] On the existence of homoclinic solutions of a class of discrete nonlinear periodic systems [J].

Zhou, Zhan ;

Yu, Jianshe .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (05) :1199-1212

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