Breathers and Compound Solitons in the System of Acoustic Phonons

Within the framework of the modified Korteweg-de Vries (mKdV) equation for the system of acoustic phonons, nonlinear dynamic states with a fine internal structure have been constructed, namely, breathers, breather lattices, and periodic modulated structures for the mKdV equation with "attraction"; and kinks, bound states of the kink-antikink type (compound solitons), and periodic lattices of compound solitons for the mKdV equation with "repulsion." Conditions have been analyzed under which the energetically advantageous process is the formation of compound solitons from a kink-antikink pair. The results obtained are directed toward an experimental search for new stable nonlinear localized states in the system of acoustic phonons, and toward a study of the specific features of their origin, interaction, and transformation.