  We study the dynamics of superposed nonlinear waves in coherently coupled
Gross-Pitaevskii (CCGP) equations with constant (autonomous system) and time
varying (non-autonomous system) nonlinearity co-efficients. By employing a
linear transformation, the autonomous CCGP system is converted into two
separate scalar nonlinear Schr\"odinger equations and we show that linear
superposition of different nonlinear wave solutions of these scalar equations
results into several kinds of nonlinear coherent structures namely, coexisting
rogue wave-Ma breather, Akhmediev-Ma breathers, collision and bound states of
Ma breathers and solitons. Next, the non-autonomous CCGP system is converted
into an autonomous CCGP system with a similarity transformation. We show an
interesting possibility of soliton compression and appearance of creeping
solitons for kink-like and periodically modulated nonlinearity coefficient.
