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We consider some nonlinear models describing interactions of long and short(LS) waves. Such LS models have been derived and proposed with variousmotivations, which mainly come from fluid and plasma physics. In this paper, westudy some of integrable LS models, namely, the Yajima-Oikawa equation, theNewell equation, the Ma equation, the Geng-Li equation and etc. In particular,the gauge equivalent counterparts of these integrable LS models (equations) arefound. In fact, these gauge equivalents of the LS equations are integrablegeneralized Heisenberg ferromagnet equations (HFE) with self-consistentpotentials (HFESCP). The associated Lax representations of these HFESCP aregiven. We also presented several spin-phonon equations which describe nonlinearinteractions of spin and lattice subsystems in ferromagnetic materials.

Integrable generalized Heisenberg ferromagnet equations with self-consistent potentials and related Yajima-Oikawa type equations