Multisoliton phase shifts in the case of a nonzero reflection coefficient

Abstract

We study multisoliton solutions of the Korteweg-de Vries equation in the case of a nonzero reflection coefficient. An explicit phase shift formula is derived that clearly displays the nature of the interaction of each soliton with the other ones and with the dispersive wavetrain. In particular, this formula shows that each soliton experiences in addition to the ordinary N-soliton phase shift an extra phase shift to the left caused by the collision with the dispersive wavetrain.