  We present analytical solution, which is periodic in nature, for a driven
cubic-quartic nonlinear Schr\"odinger equation (DCQNLSE) placed in a
bi-chromatic optical lattice. The solution indicates the creation of density
wave. Since, beyond mean-field contribution in quasi one dimensional and
one-dimensional geometry differs on the even exponents of the nonlinearity thus
we extend our analysis towards quadratic-cubic-quartic and quadratic-cubic
nonlinearities as well. Later, we study the dynamics of DCQNLSE. Our study
indicates the existence of stripe phase along with considerable phase
coherence. These findings allow us to comment on the possible emergence of
supersolid phase in a condensate.
