Mathematical Physics, Analysis and Geometry

, Volume 12, Issue 3, pp 287–324

Long-Time Asymptotics for the Korteweg–de Vries Equation via Nonlinear Steepest Descent


DOI: 10.1007/s11040-009-9062-2

Cite this article as:
Grunert, K. & Teschl, G. Math Phys Anal Geom (2009) 12: 287. doi:10.1007/s11040-009-9062-2


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.


Riemann–Hilbert problemKdV equationSolitons

Mathematics Subject Classifications (2000)

Primary 37K4035Q53Secondary 37K4535Q15

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaWienAustria
  2. 2.International Erwin Schrödinger Institute for Mathematical PhysicsWienAustria