The formally variable separation approach for the dust-acoustic solitary waves with dust charge variation

The formally variable separation approach is used for handling the dust-acoustic solitary waves in a dusty plasma, including consideration of dust charge variation. New analytical solutions of nonlinear waves are formally derived for the governing equation of the system. We have triumphantly derived the exact analytical expressions and some approximate expressions of the nonlinear dust-acoustic waves in a dusty plasma under some special cases. The work introduces entirely new solutions and emphasizes the power of the newly developed method that can be used in problems with identical nonlinearities.