Nonlinear formulation of slow Alfvén wave in magnetized plasma which can be an essential ingredient of the solar space plasma is being studied. Various method has been adopted, mathematical formulation of the magnetohydrodynamic (MHD) waves can interpret the astrophysical phenomena happening in space plasma. The mathematical formulation of slow Alfvén wave and kinetic Alfvén wave (KAW) has been done from Maxwell equation as a make model equation. On the perturbation of slow Alfvén wave by pumped wave, the coupled wave dynamics has studied and their numerical simulation has been performed at theta =50 degree. Several localized filamentary structures have observed with diverse intensities. The spectra associated with magnetic field fluctuations are also observed with Kolmogorov scaling for inertial and dispersive range spectral index which are proportional to k-5/3 and k-3 respectively.