Non-linear dynamics of coupled chains of particles

I. Sh Akhatov, V. A. Baikov, K. R. Khusnutdinova

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12 Citations (Scopus)


The equations of motion of two linear periodic chains of non-linearly interacting particles are considered in the long-wave approximation. The system of equations obtained is a model for describing wave processes in two-component media. Methods of group analysis (see, for example, [1]) are used to pick out the submodels that admit of the largest group of point mappings. Particular invariant solutions are presented resented for two submodels with obvious mechanical interpretations. It is shown that, if the potential of the non-linear interaction can be expressed as a harmonic function of the relative displacement of particles in the chains, and the acoustic velocities of non-interacting chains are different, the system is a special type of soliton filter; the allowed soliton velocities are determined. A few solutions describing the long-wave dynamics of the system are presented, assuming the presence of additional shear forces.

Original languageEnglish
Pages (from-to)353-361
Number of pages9
JournalJournal of Applied Mathematics and Mechanics
Issue number3
Publication statusPublished - 1995
Externally publishedYes


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