This research report, authored by Haruichi WASHIMI and Tosiya TANIUTI, investigates the propagation of ion acoustic solitary waves of small amplitude in a collisionless plasma of cold ions and warm electrons. The authors show that under certain approximations, the governing system of equations can be reduced to the Kortweg-deVries (KdV) equation. They derive the KdV equation by transforming the original system into a form suitable for perturbation analysis, using a small parameter ε. The derived KdV equation describes the long-time asymptotic behavior of these waves, similar to how Gardner and Morikawa described hydromagnetic waves in cold plasmas. The report also highlights the similarities between ion acoustic waves and hydromagnetic waves, particularly in their propagation directions and the orientation of magnetic fields.This research report, authored by Haruichi WASHIMI and Tosiya TANIUTI, investigates the propagation of ion acoustic solitary waves of small amplitude in a collisionless plasma of cold ions and warm electrons. The authors show that under certain approximations, the governing system of equations can be reduced to the Kortweg-deVries (KdV) equation. They derive the KdV equation by transforming the original system into a form suitable for perturbation analysis, using a small parameter ε. The derived KdV equation describes the long-time asymptotic behavior of these waves, similar to how Gardner and Morikawa described hydromagnetic waves in cold plasmas. The report also highlights the similarities between ion acoustic waves and hydromagnetic waves, particularly in their propagation directions and the orientation of magnetic fields.