Sine-Lattice Equation. II. Nearly Integrable Soliton Properties of π-Kinks and Sonic π-Kinks
1986 年 55 巻 8 号 p. 2547-2561
詳細
1986 年 55 巻 8 号 p. 2547-2561
Two non-trivial versions, S(un)−\ddotun=(g⁄2) sin (2un) and S(un)−\ddotun=0 with S(un)≡sin (un+1−un)−sin (un−un−1), of a sine-lattice (SL) equation S(un)−\ddotun=g sin un are studied. The latter is a new sort of nonlinear equation in which “sonic” π- and 2π-kinks arise from the sine-second difference S(un) rather than the on-site term sin (un) or sin (2un). In their bilinear operator form the former and the latter yielding π-kinks have much neater form than the SL equation. These two equations exhibit approximate, but well-defined, one-and multi-π-kink solutions having one-to-one correspondence to those of the sine-Gordon equation, thus possessing nearly integrable soliton properties for the π-kinks. A numerical calculation of one- and two-kink solutions is made to illustrate this for kinks of narrow width and/or high velocity.
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