Math. Phys. Anal. Geom. 12, 287-324 (2009) [DOI: 10.1007/s11040-009-9062-2]
Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.