Pattern formation in systems with nonlocal interactions

One-dimensional lattices with harmonic coupling between neighboring lattice sites and an on-site anharmonic potential V()=A²ⁿ⁺² + ⁿ⁺² + C² + D are examined in the displacive limit. Kink solutions, interpolating between the coexistent phases =0 and =±(C/A)^1/2n at theT=0 first-order phase transition pointB ²=4AC,A, C>0,B<0,D=0 are found in simple analytic form and their dependence on the degree of anharmonicity (n=2, 4, 6, ...) is discussed. It is shown that, at the phase transition point, the kinks are accompanied by a continuous spectrum of periodic nonlinear excitations (periodons) having finite energy density.Work supported by the Swiss National Science Foundation