Derivation of the K-dV Equation for Ion Acoustic Wave without Using Reductive Perturbation Method.

The K-dV equation for ion acoustic wave is derived without using the reductive perturbation method or the multiple-time-scale perturbation method. The only assumptions adopted in deriving the K-dV equation from the continuity, momentum and the Poisson equation are that: (1) the ion speed is low; and (2) the charge separation in plasmas is weak.