Abstract: Assume that the solution of KdV reflective initial value problem equals the sum of the pure-soliton part and the non-soliton part, and the latter is comparatively small. Then the equation satisfied by the non-soliton part is linearized and the solution of asymptotic oscillation form is obtained directly by means of Fourier Transformation. After solving the discrete spectrum of the time-independent Schodinger equation associated with the initial value by some proper method, the pure-soliton expression is available according to 1ST. Through the calculation of specific initial value examples, the results obtained in this paper are found to be consistent with those of the references.

Key words: initial problem, soliton, KdV equation, oscillatory tail