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Dag Nilsson: Existence and decay of lump solutions of the fractional KP equation

Time: Thu 2023-09-28 11.00 - 12.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Dag Nilsson, Lund University

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The Kadomtsev–Petviashvili equation (KP equation) is a model equation that can be used to describe three-dimensional mainly unidirectional long waves of small amplitude. In this talk I will consider the fractional Kadomtsev–Petviashvili equation (fKP equation), which is a generalization of the classical KP equation involving a fractional derivative. As inte the case of the classical KP-equation, the fKP equation comes in two versions: fKP-I (strong surface tension) and fKP-II (weak surface tension). In the talk I will outline how to prove existence of lump solutions (travelling wave solutions which decay to zero in all horizontal directions) for the fKP-I equation. I will also discuss the smoothness and decay of these lump solutions.

This talk is based on a joint work with Handan Borluk (Ozyegin University) and Gabriele Brüll (Lund University).