Periodic travelling waves in a non-integrable one-dimensional lattice

Details Periodic travelling waves in a non-integrable one-dimensional lattice Periodic travelling waves in a non-integrable one-dimensional lattice

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28..119v&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 7th, Oberwolfach, West Germany, Aug. 24-28, 1981.) Celestial Mechani

Mathematics

4

Lattices (Mathematics), Longitudinal Waves, Particle Interactions, Periodic Functions, Traveling Waves, Branching (Mathematics), Particle Energy, Sine Waves, Solitary Waves

Scientific paper

The existence of a one-parameter family of periodic solutions representing longitudinal travelling waves is established for a one-dimensional lattice of identical particles with nearest-neighbour interaction. The potential is not given in closed form but is specified by only a few global properties. The lattice is either infinite or consists of N particles on a circle with fixed circumference. Waves with low energy are sinusoidal and their properties are studied using bifurcation methods. Waves of high energy, however, are of solitary type, i.e. the excitation is strongly localized.

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