Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike   Initial Data
  We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation with steplike initial data. 
Iryna Egorova, Zoya Gladka, Volodymyr Kotlyarov, and Gerald Teschl
nlin.SI math.AP