Effect of second ion temperature on modulation stability of dust-acoustic solitary waves with dust charge variation

The derivative expansion perturbation method is applied to a cold plasma system consisting of dust grains with varying dust charge, electrons, and two species of ions with different temperatures. The basic system of equations is reduced to a nonlinear Schrödinger-type equation. The effect of the temperature of low temperature ions on the system parameters, e.g., angular frequency, group velocity, dispersion coefficient, and nonlinear coefficient, is investigated. It is found that the presence of low-temperature ions enhances the stability of the system. The small wave number limits of the coefficients of the nonlinear Schrödinger-type equation are found to agree exactly with the coefficients of the nonlinear Schrödinger-type equation obtained from the oscillatory solution of the Korteweg-de Vries equation of the system.