Dust ion acoustic freak waves in a plasma with two temperature electrons featuring Tsallis distribution

We present an investigation for the nonlinear dust ion acoustic wave modulation in a plasma composed of charged dust grains, two temperature (cold and hot) nonextensive electrons and ions. For this purpose, the multiscale reductive perturbation technique is used to obtain a nonlinear Schrödinger equation. The critical wave number, which indicates where the modulational instability sets in, has been determined precisely for various regimes. The influence of plasma background nonextensivity on the growth rate of modulational instability is discussed. The modulated wavepackets in the form of either bright or dark type envelope solitons may exist. Formation of rogue waves from bright envelope solitons is also discussed. The investigation indicates that the structural characteristics of these envelope excitations (width, amplitude) are significantly affected by nonextensivity, dust concentration, cold electron-ion density ratio and temperature ratio.