Note on Asymptotic Solutions of the Korteweg‐de Vries Equation with Solitons

摘要

The long time asymptotic solution of the Korteweg‐de Vries equation containing both solitons and the dispersive wavetrain is described. It is shown that a soliton interacts elastically both with the dispersive wavetrain and with other solitons. An explicit formula for the phase shift produced upon interaction is given. These ideas also apply to other nonlinear evolution equations solvable by the inverse scattering transfor