It is demonstrated that a description of the effects of higher-order dispersion of continuous oscillations calls for a consideration of interactions with the nearest and more distant neighbors in a crystal lattice. Exact soliton and periodic solutions of the nonlinear equation with fourth-order derivatives describing long-wavelength collective excitations in a quasi-one-dimensional chain have been found.Interest in the study of special features of nonlinear excitation propagation in systems with dispersion has quickened in the past few years [1-3]. These investigations find application, for example, in the theory of structural phase transitions in ferroelectrics caused by displacements of the equilibrium positions of atoms [4][5][6][7]. Frequencies of oscillatory modes in these systems decrease sharply when the temperature of the system approaches the critical one. As a result, ordered local regions arise that manifest themselves as additional peaks in neutron scattering [8].A theoretical description of such systems is based on the model of quasi-one-dimensional chain of identical oscillators [4]. The model suggests that each oscillator corresponds to a particle of mass m moving in a symmetric external potential field. Below we consider two sublattices, with heavy atoms of the first sublattice spaced at distance a and light atoms of mass m of the second sublattice displaced by u n from the heavy atoms.As is well known, the long-wavelength limit in the description of mechanics of a discrete system based on the use of differential equations with the second-order spatial derivatives remains unchanged for arbitrary number of interacting neighbors. Therefore, this approximation can be developed on the basis of the model considering interactions with the nearest neighbors with inclusion of the interparticle interaction parameter. If higher-order dispersion is considered, it will be described by an independent parameter. This parameter arises if we consider interactions with the nearest and more distant neighbors in the crystal lattice. This approach was first examined in [9,10].With allowance for the foregoing, we now include terms describing the potential energy of interactions with the second neighbors into the Hamiltonian. Then the model Hamiltonian of the examined system assumes the form 2 2 2 1 1 2 2