Equilibrium nonlinear distributions of one-component order parameter in systems with competitive interaction

The approach which enables to obtain the solutions of the variational equation as the series [phi'(x)](2) = Sigma(n=0)(N) a(n) phi(2n) is considered. It is shown that when N = 1 it gives well-known cos x solutions, while for N > 1 it leads to essentially nonlinear functions. The phi(2) phi(2)'-term in the thermodynamical potential provides the proper nonlinear behavior of the order parameter and the possibility of existence of kink-like distributions, particularly. In special case N = 2 there exist the exact partial solutions which, however, do not give the absolute minima to the thermodynamical potential.