Some properties of dynamic solitons of nonlinear systems that are determined by the linearized equation

The features of dynamic solitons in nonlinear systems described by differen tial equations with fourth-order spatial derivatives are discussed for syst ems of different dimensionalities. The existence conditions for a nonradiat ive soliton are formulated for the case when the internal frequency of the soliton lies in the continuous spectrum of harmonic oscillations of the sys tem under study. These conditions are determined by the form of the dispers ion relation of the linear oscillations. The use of the stated conditions f or determining the parameters of two-dimensional solitons is demonstrated. (C) 2000 American Institute of Physics. [S1063-777X(00)01406-7].