One-dimensional nonlinear Schroedinger equation: A nonlinear dynamical approach

Journal Article · Mon Jan 15 00:00:00 EST 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.41.800· OSTI ID:7160623

Wan, Y; Soukoulis, C M ^[1]

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1. Ames Laboratory and Department of Physics Iowa State University, Ames, Iowa 50011 (USA)

We have studied a time-independent nonlinear Schroedinger equation of the tight-binding form on a one-dimensional lattice. The real and complex wave functions as solutions to the equation are considered separately for different physical problems. For each case, an area-preserving map for the discrete nonlinear Schroedinger equation is introduced and analyzed. The bounded solutions can be organized in hierarchies composed of periodic, quasiperiodic, as well as chaotic orbits on the phase plane of the nonlinear map. A stability-zone'' diagram, where the bounded orbits exist, is displayed in the parameter space, serving as phase diagram'' of the nonlinear Schroedinger equation under appropriate boundary conditions. Studies of the stability zone yield useful information for the physical problems considered. The periodic orbits and their stabilities can be obtained by a convergent perturbation method. Finally, we remark on several physical problems where these results might be applicable. In particular, we discuss the stabilities of the large polaron solution in the Holstein model.

• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 7160623
• Journal Information: Physical Review, A (General Physics); (USA), Vol. 41:2; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
SCHROEDINGER EQUATION
ANALYTICAL SOLUTION
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
POLARONS
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
WAVE EQUATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics