Approximate (Asymptotically Exact) Solutions for Anharmonic Localized Modes and Vortexlike Modes and Exact Static Vortexlike Mode Solutions in the D-Dimensional Sine-Lattice Equation.

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  • Takeno Shozo
    Laboratory of Physics, Faculty of Engineering and Design, Kyoto Institute of Technology, Kyoto 606
  • Hori Kazunari
    Laboratory of Physics, Faculty of Engineering and Design, Kyoto Institute of Technology, Kyoto 606
  • Ohtsuka Kazushi
    Laboratory of Physics, Faculty of Engineering and Design, Kyoto Institute of Technology, Kyoto 606
  • Homma Shigeo
    Department of Physics, Faculty of Engineering, Gunma University, Kiryu 376

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  • Approximate Asymptotically Exact Soluti
  • Approximate (Asymptotically Exact) Solutions for Anharmonic Localized Modes and Vortexlike Modesand Exact Static Vortexlike Mode Solutions in the<i>D</i>-Dimensional Sine-Lattice Equation

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An analytical study is made to seek intrinsic nonlinear-mode solutionsto the d-dimensional sine-lattice (SL) equation\begin{equation}∑i Ji {sin[u(n+ ei)-u(n)]- sin[u(n)-u(n - ei)]}-[∂ 2u(n)/∂ t2]=(λ /2) sin[2u(n)]\end{equation}with λ >0 or λ =0 in the form u(n)=2 tan-1[f(k · n-ω t)/g( K· n-{Ω}t)] with κ =(κ1, , κ2, · · ·, , κd)(κ =k, , K), where f and g are trigonometric or hyperbolic functions. Approximate analytical solutions for moving and stationary anharmonic localized modes and vortexlike modes (d>2) are obtained for | ki| << 1 and | Ki| << 1. For λ =0, exact static vortexlike mode solutions exist provided the ki's and the Ki's satisfy certain specific conditions. For d=1, numerical experiments are performed to confirm the existence of the asymptotically exact moving anharmonic localized modes in the SL equation for λ =0.

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