An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries (KdV) equation.

@article{Deift1998AnEO,
  title={An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries (KdV) equation.},
  author={Percy Deift and Stephanos Venakides and Xin Zhou},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1998},
  volume={95 2},
  pages={450-4}
}
This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way. We present, in particular, an algorithm, to obtain the support of the Riemann-Hilbert problem for leading asymptotics. Applying this extended method to small dispersion KdV (Korteweg-de Vries) equation, we (i) recover the… CONTINUE READING