Two non-trivial versions,
S(
un)−\ddot
un=(
g⁄2) sin (2
un) and
S(
un)−\ddot
un=0 with
S(
un)≡sin (
un+1−
un)−sin (
un−
un−1), of a sine-lattice (SL) equation
S(
un)−\ddot
un=
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 (2
un). 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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