The Exact <i>N</i>-Soliton Solution of the Korteweg-de Vries Equation

The exact N -soliton solution of the Korteweg-de Vries equation is obtained through the procedure suggested by Gardner, Greene, Kruskal and Miura. From this solution, it is shown that solutions are stable and behave like particles. The collisions are well described by the phase shifts. Explicit calculation of the phase shifts assures the conservation of the total phase shift. This fact turns out to be a special expression for the constant motion of he center of mass.