Sine-Lattice Equation. III. Nearly Integrable Kinks with Arbitrary Kink Amplitude

Abstract

A sine-lattice equation sin (u_n+1−u_n)−sin (u_n−u_n−1)−\ddotu_n=0 is shown both analytically and numerically to exhibit approximate, but well-defined, one- and multi-kink solutions of the form u_n=A tan⁻¹(α_n⁄β_n) for an arbitrary constant A>0, where the quantities α_n and β_n are simply discrete versions of the corresponding ones in the conventional sine-Gordon equation. This is due to the kink dispersion relation 4 sinh²(k⁄2)−ω²=0 entirely equal to the case of the Toda lattice solitons.