The Existence of Solutions for the Problem in the Optical Lattice with Nonlocal Nonlinearity

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discuss the solitons solution for a class of nonlinear SchrSdinger equations in the optical lattice with nonlocal nonlinearity. We also sho...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 28; no. 4; pp. 681 - 690
Main Authors Zhang, Rui-feng, Liu, Ren-tao
Format Journal Article
LanguageEnglish
Published Heildeberg Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.10.2012
Subjects
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
先验估计
光学晶格
初始问题
孤子解
局部非线性
解的存在性
非局域性
非线性介质
contract mapping principle
Galerkin method
35B40
35K57
Schrödinger equation
Cauchy problem
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Summary:We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discuss the solitons solution for a class of nonlinear SchrSdinger equations in the optical lattice with nonlocal nonlinearity. We also show via a uniform priori estimate that existence and uniqueness of the global solution for the initial problem.
Bibliography:11-2041/O1
We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discuss the solitons solution for a class of nonlinear SchrSdinger equations in the optical lattice with nonlocal nonlinearity. We also show via a uniform priori estimate that existence and uniqueness of the global solution for the initial problem.
SchrSdinger equation, Cauchy problem, contract mapping principle, Calerkin method
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-012-0182-2