一个微分差分方程的N-孤子解及动力分析  

N-solitons to a Differential Difference Equation and Dynamics

作　　者：李琪[1] 张文[1] 

机构地区：[1]东华理工大学理学院,江西抚州344000

出　　处：《东华理工大学学报（自然科学版）》2014年第3期344-347,共4页Journal of East China University of Technology(Natural Science)

基　　金：江西省教育厅科技项目(GJJ13459);江西省自然科学基金(20142BAB201006);国家自然科学基金(41001320)

摘　　要：非线性薛定谔方程具有深刻的应用背景,特别是近年来在金融数学领域出现了连续、离散、耦合和向量非线性薛定谔方程。研究这类方程的解可以对实际问题模型进行定量分析和预测。非线性薛定谔方程可视为Ablowitz-Kaup-NewellSegu(AKNS)谱问题的相容性条件,离散非线性薛定谔方程可视为离散Ablowitz-Ladik谱问题的相容性条件。本文给出联系于离散Ablowitz-Ladik谱问题的一个微分差分方程及其Lax对,通过Hirota方法找到N-孤子解,分析单孤子运动和双孤子相互作用的动力特征.The Schrdinger equations models much physcial phenomena. Besides,the discrete and continuous including coupled and vector Nonlinear Schrdinger Systems are found recently in the financial mathematics. The discrete nonlinear Schrdinger equation can be regarded as a compatibility condition of the discrete Ablowitz-Ladik spectral problem. In the paper,a differential difference equation is considered,which is another compatibility condition of the discrete Ablowitz-Ladik spectral problem. N-solitons to the differential difference equation are given and the dynamics are analyzed.

关 键 词：离散Ablowitz-Ladik谱问题 LAX对 HIROTA方法 N-孤子解 

分 类 号：O175[理学—数学]