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We discuss the quasiclassical approximation for the equations of motions of anonlinear chain of phonons and electrons having phonon mediated hopping.Describing the phonons and electrons as even and odd grassmannian functions andusing the continuum limit we show that the equations of motions lead to aZakharov-like system for bosonic and fermionic fields. Localised andnonlocalised solutions are discussed using the Hirota bilinear formalism.Nonlocalised solutions turn out to appear naturally for any choice of waveparameters. The bosonic localised solution has a fermionic dressing while thefermionic one is an oscillatory localised field. They appear only if someconstraints on the dispersion are imposed. In this case the density of fermionsis a strongly localised travelling wave. Also it is shown that in the multiplescales approach the emergent equation is linear. Only for the resonant case weget a nonlinear fermionic Yajima-Oikawa system. Physical implications arediscussed.Comment: 7 pages, LaTeX, no figures. to appear in Europhysics Latter

Localised and nonlocalised structures in nonlinear lattices with fermions