Dynamicl Character for a Perturbed Coupled Nonlinear SchrL dinger System
-
摘要: 研究具周期边界条件的扰动非线性Schrdinger方程组的动力性态,首先,在常值平面上用线性算子的谱对扰动和未扰动系统进行动力性态分析,然后利用奇异扰动理论和不动点原理证明局部不变流形的存在性.
-
关键词:
- 非线性Schrdinger方程组 /
- 动力性态 /
- 不变流形
Abstract: The dynamics for a perturbed coupled nonlinear SchrL dinger system with periodic boundary condition was studiesd. First, the dynamics of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the sigular perturbation theory and the fixed-point argument.-
Key words:
- coupled nonlinear SchrL dinger system /
- dynamics /
- invariant manifold
-
[1] Ablowitz M J,Ohta Y,Trubatch A D.On discretizations of the vector nonlinear schrdinger equation[J].Physics Letter A,1999,253(5/6):287—304. doi: 10.1016/S0375-9601(99)00048-1 [2] Ablowitz M J,Ohta Y,Trubatch A D.On integrability and chaos in discrete systems[J].Chaos Solitons Fractals,2000,11(1/3):159—169. doi: 10.1016/S0960-0779(98)00280-X [3] Yang J,Tan Y.Fractal dependence of vector-soliton colli-sions in birefringent fibers[J].Physics Letter A,2001,280(3):129—138. doi: 10.1016/S0375-9601(01)00040-8 [4] Li Y,Mclaughlin D W,Shattah J,et al.Persistent homoclinic orbits for a perturbed nonlinear Schrdinger equation[J].Communication on Pure and Applied Mathematics,1996,49(11):1175—1255. doi: 10.1002/(SICI)1097-0312(199611)49:11<1175::AID-CPA2>3.0.CO;2-9 [5] Wright Otis C,Forest Gregory M.On the backlund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrodinger system[J].Physica D,2000,141(1/2):104—116. doi: 10.1016/S0167-2789(00)00021-X [6] Forest M G,McLaughlin D W,Muraki D J,et al.Nonfocusing instabilities in coupled integrable nonlinear Schrodinger PDEs[J].Journal Nonlinear Science,2000,10(3):291—331. doi: 10.1007/s003329910012 [7] Forest M G,Sheu S P,Wright O C.On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrodinger systems[J].Physics Letters A,2000,266(1):24—33. doi: 10.1016/S0375-9601(00)00018-9
计量
- 文章访问数: 2313
- HTML全文浏览量: 103
- PDF下载量: 627
- 被引次数: 0