A semi-discrete modified KdV equation

摘要

In this paper, we present an integrable semi-discretization of the modified Kortewegd-eVries (mKdV) equation. We discretize the "time" variable of the mKdV equation and get an integrable differential-difference system. Under a standard limit, the differential- difference system converges to the continuous mKdV equation. By Hirota's bilinear method, we find some explicit solutions including solitons and breather solutions. From the semi-discrete system, we design a numerical scheme to the mKdV equation and carry out several numerical experiments with the 3-soliton solution and breather solution. Published by AIP Publishing.