Periodic metastable structures in the discrete straight phi4 model

For the discrete straight phi(4) model a class of metastable periodic solutions is given in the form of Fourier series. From the symmetry consideration, we eliminate the harmonics with zero amplitudes and thus, reduce the number of degrees of freedom. For the rest of harmonics we establish the hierarchy of their significance. For solutions with a small period we give the exact expression of energy density in terms of amplitudes of harmonics. Conditions of existence and stability of the solutions are discussed. For some limiting cases the approximate solutions of different kinds are given. The analytical results are compared with the results of numerical study. We also discuss a mechanism of transition from a metastable periodic structure into the ground state and apply the results to the lock-in transition in dielectric crystals supporting incommensurate phase.