On asymptotic results in the theory of integrable partial differential equations
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
I will consider the Cauchy problem for several integrable partial differential equations like the Korteweg de Vries equation, the modified Korteweg de Vries equation and the nonlinear Schroedinger equation and study the properties of their solutions in two asymptotic regimes :
1. long time asymptotic limit,
2. semiclassical or small dispersion limit.
I will explain how the integrability of the equations enables to give an explicit asymptotic description of the solution and I will argue that in some cases, such description persists beyond the integrable cases.
- Tamara GRAVA