  Quantum corrections to nonlinear ion acoustic wave with Landau damping have
been computed using Wigner equation approach. The dynamical equation governing
the time development of nonlinear ion acoustic wave with semiclassical quantum
corrections is shown to have the form of higher KdV equation which has higher
order nonlinear terms coming from quantum corrections, with the usual classical
and quantum corrected Landau damping integral terms.
  The conservation of total number of ions is shown from the evolution
equation. The decay rate of KdV solitary wave amplitude due to presence of
Landau damping terms has been calculated assuming the Landau damping parameter
$\alpha_1 = \sqrt{{m_e}/{m_i}}$ to be of the same order of the quantum
parameter $Q = {\hbar^2}/({24 m^2 c^2_{s} L^2})$. The amplitude is shown to
decay very slowly with time as determined by the quantum factor $ Q$.
