ANuI

 
 

Dispersive partial differential equations (PDEs) have important applications such as hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. This project will study these PDEs, mainly in higher dimensions, using a ground-breaking combination of analytic and numerical approaches and techniques from the theory of integrable systems, which can also be applied to non- integrable PDEs. The goal is to use the predictive power of numerical techniques to achieve breakthroughs in analytical techniques, while deploying analytical insights to generate innovative numerical schemes with broader applications. 



The dispersive equations considered here can have special solutions as solitons and breathers which can appear in the long time asymptotics of the equations. Moreover, solutions can have a blow-up in finite time, i.e., a loss of regularity, which is challenging from both an analytic and a numerical point of view. This is important in applications, as it indicates the limits of the approximations made in describing a situation via the studied model.


 

Participants

  1. C.Klein (coordinator, Dijon)

F. Achleitner (Wien)

  1. A.Kazeykina (Orsay)

Phd students

  1. E.Duboquet (Dijon)

H. Luong (Wien)


Selected Figures




 

Analytical, Numerical and Integrable systems approaches for nonlinear dispersive partial differential equations