Nonlinear Lattice Dynamics Of Atomic Chains

AbstractThe nonlinear localized mode of perfect lattice has become anew popular investigating field of lattice dynamics last severalyears. As to theory analysis, much atteniion has usually beenlargely paid to a monatomic chain, because of itS simPle model, itsclear physics image and the exiting various linear or nonlinearelementary excitations. Research showed that it exhibits intrinsiclocalized mode in a monatomic chain with the nearest-neighborharmonic and cubic, quartic anharmonic interaction. That is, thereexits envelope, envelope-kink, envelope-antikink solitons in thechain. Since the theory what the lattice dynamics of a monatomicchain with nearest-neighbor interaction has been matllred, the issueof lattice dynamics of a monatomic chain with higher anhimonicand long-range interaction, especial with second nearest-neighborinteraction, Iooks like more important.In this paPer, lattice dynamics of a monatomic chain arestudied by employing the method of multiple scales combined withquasi-discreteness aPproximation. We get CMKdV and PDNLSequations of the one-dimensiona1 lattices and obtain a series ofdynamic properties of soliton in the monatomic chain. The thesisconsists of five chapters. ln chapter l, we mainly introducefundamental theories about the developed process of soliton, themethod of multiple scales combined with quasi-discretenessapproximation and other relative methods. In chaPter 2, thesemethods are emPloyed to inveStigate the wave motive equation of amonatomic chain Wth second nearest-neighbor harmonic andquartic anharmonic interactions get a new linear dispersion relation.Further more, we first obtain the CMKdV equation of themonatomic chain. Then, soliton of the chain with second nearest-neighbor harmonic, cubic and quartic anharmonic interactions are discussed explain our result show that the kink amplitude of the self-localized structures are determined only by the intrinsic properties of its lattices, which is agreement with the experimental phenomena. In chapter 3, we study monatomic chain with power-law long-range interactions and get non-propagating intrinsic localized mode in other wave-vector as well as that in the boundary of the phonon Brillouin zone. There are 1 point non-propagating soliton in the phonon Brillouin zone when considering the lth nearest-neighbor inter-actions. In chapter 4, we investigated the behavior of wave in a nonlinear monatomic chain with damping. Parameter dissipation nonlinear Schrodinger (PDNLS) equation of lattice dynamics is first obtained. Then we discuss effect of damping on soliton of monatomic chain. In last chapter, our results are summarized and studied prospects are made out.