Periodic and decaying solutions in discrete nonlinear Schrodinger with saturable nonlinearity

被引：67

作者：

Pankov, Alexander ^{[2
]}

Rothos, Vassilis ^{[1
]}

机构：

[1] Aristotle Univ Thessaloniki, Fac Engn, Sch Math Phys & Computat Sci, Thessaloniki 54124, Greece

[2] Morgan State Univ, Dept Math, Baltimore, MD 21251 USA

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2008年 / 464卷 / 2100期

关键词：

periodic and decaying solutions; discrete nonlinear Schrodinger; the Nehari manifolds;

D O I：

10.1098/rspa.2008.0255

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We demonstrate the existence of solutions in the discrete nonlinear Schrodinger equation (DNLS) with saturable nonlinearity. We consider two types of solutions to DNLS periodic and vanishing at infinity. Calculus of variations and the Nehari manifolds are employed to establish the existence of these solutions. We present some extensions of our results, combining the Nehari manifold approach and the Mountain Pass argument.

引用

页码：3219 / 3236

页数：18

共 50 条

[1] Doubly periodic waves of a discrete nonlinear Schrodinger system with saturable nonlinearity
Conte, Robert
Chow, K. W.
[J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2008, 15 (04) : 398 - 409
[2] Exact and explicit solutions to the discrete nonlinear Schrodinger equation with a saturable nonlinearity
Aslan, Ismail
[J]. PHYSICS LETTERS A, 2011, 375 (47) : 4214 - 4217
[3] On the existence of gap solitons in a periodic discrete nonlinear Schrodinger equation with saturable nonlinearity
Zhou, Zhan
Yu, Jianshe
Chen, Yuming
[J]. NONLINEARITY, 2010, 23 (07) : 1727 - 1740
[4] Thresholds for breather solutions of the discrete nonlinear schrodinger equation with saturable and power nonlinearity
Cuevas, J.
Eilbeck, J. C.
Karachalios, N. I.
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2008, 21 (02) : 445 - 475
[5] Ground state solutions for periodic discrete nonlinear Schrodinger equations with saturable nonlinearities
Zhang, Luyu
Ma, Shiwang
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[6] Exact solutions of the two-dimensional discrete nonlinear Schrodinger equation with saturable nonlinearity
Khare, Avinash
Rasmussen, Kim O.
Samuelsen, Mogens R.
Saxena, Avadh
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (37)
[7] Exact solutions for a system of two coupled discrete nonlinear Schrodinger equations with a saturable nonlinearity
Kol, Guy Richard
Woafo, Paul
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (11) : 5956 - 5962
[8] Exact solutions of the saturable discrete nonlinear Schrodinger equation
Khare, A
Rasmussen, KO
Samuelsen, MR
Saxena, A
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (04): : 807 - 814
[9] Envelope solution profiles of the discrete nonlinear Schrodinger equation with a saturable nonlinearity
Yan, Zhenya
[J]. APPLIED MATHEMATICS LETTERS, 2009, 22 (04) : 448 - 452
[10] Gap solitons in periodic discrete nonlinear Schrodinger equations with saturable nonlinearities
Pankov, Alexander
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 371 (01) : 254 - 265

← 1 2 3 4 5 →