This paper presents the study of a nonlinear process in solar corona where the dispersive Alfvén waves (DAW) may lead to coronal heating. The model equations governing the nonlinear excitation of the fast waves (FW) by DAW in the low-beta plasmas (applicable to solar corona) are given. By taking proper account of the ponderomotive nonlinearity, we have set up the equations for the decay waves namely the FW and another DAW. The expressions for the coupling coefficients of the three wave interaction have been derived. The growth rate of the instability is also calculated and found that the value of the decay growth time comes out to be of the order of milliseconds at the pump DAW amplitude B0y/B0=10-3. This time scale is much shorter than the observed time scales (minute or less) in the coronal heating process as seen by Yohkoh and SOHO.