Starting from the nonlinear equation describing a non-local interaction of dipoles along 1D chain [1] we derive a differential nonlinear equation which is a good approximation for the integral equation in the case of the short-range non-locality. The derived equation coincides with the generalized sine-Gordon equation proposed in Ref.[2]. The kink-like analytical solutions of the equation under consideration are known [2]. Using the asymptotic perturbation method we present analytical solutions of the two-parametrical dynamical soliton type and a bound state of kink-like solitons. It is found the solitons can transform into compactons in a special limiting case.
[1] L.Vazquez, W.A.B.Evans, G.Rickayzen, Phys.Lett.A189 (1994) 454.
[2] H.Zorski and E.Infeld, Phys.Rev.Lett. 68 (1992) 1180.