Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2004-06-21
Nonlinear Sciences
Exactly Solvable and Integrable Systems
7 pages, LaTeX, no figures. to appear in Europhysics Latters
Scientific paper
10.1209/epl/i2004-10088-6
We discuss the quasiclassical approximation for the equations of motions of a nonlinear chain of phonons and electrons having phonon mediated hopping. Describing the phonons and electrons as even and odd grassmannian functions and using the continuum limit we show that the equations of motions lead to a Zakharov-like system for bosonic and fermionic fields. Localised and nonlocalised solutions are discussed using the Hirota bilinear formalism. Nonlocalised solutions turn out to appear naturally for any choice of wave parameters. The bosonic localised solution has a fermionic dressing while the fermionic one is an oscillatory localised field. They appear only if some constraints on the dispersion are imposed. In this case the density of fermions is a strongly localised travelling wave. Also it is shown that in the multiple scales approach the emergent equation is linear. Only for the resonant case we get a nonlinear fermionic Yajima-Oikawa system. Physical implications are discussed.
Carstea Stefan Adrian
Grecu Dan
Visinescu Anca
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