A Sine-Lattice(Sine-Form Discrete Sine-Gordon)Equation--One-and Two-Kink Solutions and Physical Models

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  • Takeno Shozo
    Department of Physics, Faculty of Engineering and Design, Kyoto Institute of Technology
  • Homma Shigeo
    Department of Applied Physics, Faculty of Engineering, Nagoya University

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タイトル別名
  • A Sine-Lattice (Sine-Form Discrete Sine-Gordon) Equation —One-and Two-Kink Solutions and Physical Models—
  • A Sine Lattice Sine Form Discrete

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A sine-lattice (SL) (sine-form discrete sine-Gordon) equation defined as sin (un+1−un)−sin (un−un−1)−\ddotun=g sin un is studied. By introducing a dependent variable transformation and the Hirota D-operators, it can be recast into a bilinear operator form similar to that of the sine-Gordon (SG) equation. This shows that the SL equation is much closer in its soliton properties to the SG equation than the discrete SG equation with the difference factor un+1+un−1−2un. It is shown that the SL equation yields, though not mathematically exact, but well-defined, one-kink and specific two-kink solutions. A numerical calculation which lends support to this is also presented. Several physical models are discussed where the SL equation appears as a more natural model field equation than the discrete SG equation.

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