The paper presents a study on the propagation of ion acoustic solitary waves of small amplitude. It shows that under certain approximations, the basic system of equations governing the propagation of ion acoustic waves can be reduced to the Korteweg-de Vries (KdV) equation. The KdV equation is known for describing the behavior of solitary waves. The study compares this result with previous work on hydromagnetic waves in cold plasma. The equations governing the system include the continuity equation for ions, the momentum equation for ions, the momentum equation for electrons, and the Poisson equation. The boundary conditions are set as n = ne = 1 and u = 0 as x approaches infinity. The derivation of the KdV equation follows a similar approach to that used by Gardner and Morikawa for hydromagnetic waves. The study introduces new coordinates and expands the variables in a power series in terms of a small parameter ε. By analyzing the first and second order terms, the KdV equation is derived. The study shows that when u^(1) is a function of ξ only, the KdV equation reduces to the equation for the weak solitary wave of the original system. Linearizing the KdV equation gives the long-time asymptotic solution of the linearized original system. The paper also notes the similarity between ion acoustic waves and hydromagnetic waves in cold plasma.The paper presents a study on the propagation of ion acoustic solitary waves of small amplitude. It shows that under certain approximations, the basic system of equations governing the propagation of ion acoustic waves can be reduced to the Korteweg-de Vries (KdV) equation. The KdV equation is known for describing the behavior of solitary waves. The study compares this result with previous work on hydromagnetic waves in cold plasma. The equations governing the system include the continuity equation for ions, the momentum equation for ions, the momentum equation for electrons, and the Poisson equation. The boundary conditions are set as n = ne = 1 and u = 0 as x approaches infinity. The derivation of the KdV equation follows a similar approach to that used by Gardner and Morikawa for hydromagnetic waves. The study introduces new coordinates and expands the variables in a power series in terms of a small parameter ε. By analyzing the first and second order terms, the KdV equation is derived. The study shows that when u^(1) is a function of ξ only, the KdV equation reduces to the equation for the weak solitary wave of the original system. Linearizing the KdV equation gives the long-time asymptotic solution of the linearized original system. The paper also notes the similarity between ion acoustic waves and hydromagnetic waves in cold plasma.