涩里番

Title: Numerical approximations to nonlinear dispersive equations, from short to long times

Abstract: The first part of this talk deals with the numerical approximation to nonlinear dispersive equations, such as the prototypical nonlinear Schr枚dinger or Korteweg-deVries equations. We introduce integration techniques allowing for the construction of听 schemes which preserve the geometric structure and qualitative behavior of the equation on the discrete level. Higher order extensions will be presented, following techniques based on decorated trees series inspired by singular stochastic PDEs via the theory of regularity structures.
In the second part, we introduce a new approach for designing and analyzing schemes for some nonlinear and nonlocal integrable PDEs. This work is based upon recent theoretical breakthroughs on explicit formulas for nonlinear integrable equations. It opens the way for studying the asymptotic behavior of the solutions, with applications to the soliton resolution conjecture, and in wave turbulence theory.

听

Location : UdeM, Pavillon Andr茅-Aisenstadt, room 5183

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Meeting ID: 895 2873 0384

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