  In this paper, using a novel approach involving the truncated Laurent
expansion in the Painlev\'e analysis of the (2+1) dimensional K-dV equation, we
have trilinearized the evolution equation and obtained rather general classes
of solutions in terms of arbitrary functions. The highlight of this method is
that it allows us to construct generalized periodic structures corresponding to
different manifolds in terms of Jacobian elliptic functions, and the
exponentially decaying dromions turn out to be special cases of these
solutions. We have also constructed multi-elliptic function solutions and
multi-dromions and analysed their interactions. The analysis is also extended
to the case of generalized Nizhnik-Novikov-Veselov (NNV) equation, which is
also trilinearized and general class of solutions obtained.
