MATH Semineri: “Semi-periodic Problems for Nonlinear Integrable Evolution”, Petros Kalamvokas, 15:30 29 Nisan 2024 (EN)

You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.

Speaker: Petros Kalamvokas (Bilkent University)

“Semi-periodic Problems for Nonlinear Integrable Evolution”

Abstract: In this talk we present the solvability of a semi-periodic problem for the well known Kadomtsev–Petviashvili (KP) equation. Specifically, we consider the Cauchy problem on the cylinder (C:=S1 × R) for the KPII equation, with one temporal (t) and two spatial (x, y) independent variables, with periodicity in the x-direction and decay in the y-direction. Since this equation posses a Lax pair, the method of the inverse spectral transform is being used. For initial data with small L1 and L2 norms (and assuming the zero mass constraint), the initial-value problem is reduced to a Riemann–Hilbert problem with shift on the boundary of certain infinite strips in the complex plane of the spectral parameter. Both the direct and inverse spectral problems are being rigorously solved and we prove that the initial-value problem has a unique solution for all non-negative time t, uniformly bounded for all t in L2(C), by assuming that the initial data have small derivatives up to 8th order in the space L1(C) ∩ L2(C).

Date: Monday, April 29, 2024
Time: 15:30 – 16:30
Place: Mathematics Seminar Room SA – 141