We study the nonlinear coupling of kinetic Alfv\’{e}n waves with ion acoustic waves applicable to the Earth’s radiation belt and near-Sun streamer belt solar wind using dynamical equations in the form of modified Zakharov systems. Numerical simulations show the formation of magnetic field filamentary structures associated with density humps and dips which become turbulent at later times, redistributing the energy to higher wavenumbers. The magnetic power spectra exhibit an inertial range Kolmogorov-like spectral index value of \(-5/3\) for \(k_\perp\rho_i < 1\), followed by a steeper dissipation range spectra with indices \(\sim -3\) for the radiation belt case and \(\sim-4\) for the near-Sun streamer belt solar wind case, here \(k_\perp\) and \(\rho_i\) represent the wavevector component perpendicular to the background magnetic field and the ion gyroradius, respectively. Applying quasilinear theory in terms of the Fokker-Planck equation in the region of wavenumber turbulent spectra, we find the particle distribution function flattening in the superthermal tail population which is the signature of particle energization and plasma heating.