Effect of combined Kappa-Cairns distributed electrons on modulational instability and envelope soliton of ion-acoustic waves in electron-ion dusty plasma

Theoretical and numerical investigations are performed to study the amplitude modulation of ion-acoustic waves in an unmagnetized collisionless dusty plasma system whose components are warm ions (adiabatic), charged (negative) dust particles and Combined Kappa-Cairns distributed electrons. Modulational instability of ion-acoustic waves is analyzed through derivation of the nonlinear Schr & ouml;dinger equation using the reductive perturbation technique by implementing hydrodynamic equations for this system. The conditions for modulational instability for this electron-ion dusty plasma system have been developed, and the impacts of the relevant physical parameters on the instability region along with the maximum growth rate of instability are demonstrated. Bright and dark envelope solitons are presented, and it is observed that the profiles of envelope solitons are significantly influenced by the existence of high-energy Combined Kappa-Cairns distributed electrons.