Stability of Solitary Waves in a Model of Isotropic Composite

A problem on stability of a three-parametrical family of solitary waves in the isotropic elastic composite is considered. A model of such composite describes an elastic medium that infinitely extends in all directions with uniformly distributed elastic rods that are parallel to a direction of the wave propagation. It is proved that all the family is orbitally stable in a certain range of propagation velocities of the solitary waves. This stability problem is typical for analogous problems on stability of localized pulses in two-mode models of elastic media such as rods subjected to compression and bending.