# Jonatan Lenells: Asymptotics for the sine-Gordon equation in the quarter plane

Välkommen till en föreläsning i seminarieserien i matematik.

Jonatan Lenells

#### Titel/Title

Asymptotics for the sine-Gordon equation in the quarter plane

#### Sammanfattning/Abstract

I will discuss initial-boundary value problems for integrable PDEs. Why are they important and how can we study them? To be concrete, I will focus on the sine-Gordon equation posed in the quarter plane. After describing how this problem can be analyzed via Riemann-Hilbert techniques, I will present asymptotic formulas for the solution. Assuming that the initial and boundary values approach integer multiples of 2\pi for large x and t, we will see that the long-time behavior is described by three asymptotic sectors. Of particular interest are formulas for the topological charge of the solution and for the interaction between the asymptotic solitons and the radiation background. Paper reference: arXiv:1710.01530

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Rum D1172, hus D, Växjö