Applied Mathematics and Mechanics

, Volume 26, Issue 7, pp 823–829 | Cite as

Dynamical character for a perturbed coupled nonlinear Schrödinger system

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Abstract

The dynamical character for a perturbed coupled nonlinear Schrödinger system with periodic boundary condition was studied. First, the dynamical character 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 singular perturbation theory and the fixed-point argument.

Key words

coupled nonlinear Schrödinger system dynamical character invariant manifold 

Chinese Library Classification

O175 

2000 Mathematics Subject Classification

35Q55 

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References

  1. [1]
    Ablowitz M J, Ohta Y, Trubatch A D. On discretizations of the vector nonlinear Schrödinger equation[J].Physics Letter A, 1999,253 (5/6):287–304.MATHMathSciNetCrossRefGoogle Scholar
  2. [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.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Yang J, Tan Y. Fractal dependence of vector-soliton collisions in birefringent fibers[J].Physics Letter A, 2001,280(3):129–138.MATHCrossRefGoogle Scholar
  4. [4]
    Li Y, Mclaughlin D W, Shattah Jet al. Persistent homoclinic orbits for a perturbed nonlinear Schrödinger equation[J].Communication on Pure and Applied Mathematics, 1996,49 (11): 1175–1255.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Wright Otis C, Forest Gregory M. On the backlung-gauge transformation and homoclinic orbits of a coupled nonlinear Schrödinger system[J].Physica D, 2000,141 (1/2):104–116.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Forest M G, McLaughlin D W, Muraki D J,et al. Nonfocusing instabilities in coupled integrable nonlinear Schrödinger PDEs[J].Journal Nonlinear Science, 2000,10(3):291–331.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Forest M G, Sheu S P, Wright O C. On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems[J].Physics Letters A, 2000,266(1): 24–33.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2005

Authors and Affiliations

  1. 1.School of Computer and InformationChongqing Jiaotong UniversityChongqingP. R. China
  2. 2.Department of Applied MathematicsGuangzhou UniversityGuanzhouP. R. China
  3. 3.Institute of Applied Physics and Computational MathematicsBeijingP. R. China

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