  A nonlocal form of a two-layer fluid system is proposed by a simple symmetry
reduction, then by applying multiple scale method to it a general nonlocal two
place variable coefficient modified KdV (VCmKdV) equation with shifted space
and delayed time reversal is derived. Various exact solutions of the VCmKdV
equation, including elliptic periodic waves, solitary waves and interaction
solutions between solitons and periodic waves are obtained and analyzed
graphically. As an illustration, an approximate solution of the original
nonlocal two-layer fluid system is also given.
