We present numerical simulations of Alfv¿n waves in steady state, leading to the formation of intense magnetic filaments when the nonlinearity arises due to the ponderomotive effects and Joule heating. When the plain Alfv¿n wave is perturbed by a transverse perturbation and the magnitude of the pump Alfv¿n wave changes, chaotic filamentary structures of magnetic field in kinetic Alfv¿n wave (KAW) filamentation and quasiperiodic in inertial Alfv¿n wave (IAW) filamentation have been observed. At higher KAW pump wave amplitude, the spectra approaches near the Kolmogorov k -5/3 scaling. The spectral index becomes k -3 scaling in IAW. Relevance of these studies in solar wind and magnetosphere for KAW and solar corona and auroral region for IAW has also been pointed out. Particle heating in these small-scale filamentary structures has also been calculated by using velocity space diffusion coefficient in Fokker-Planck equation.