190 citations · 1.1k across the 82 of their papers we have counts for
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Boundary value problems for the elliptic sine-Gordon equation in a semi-strip
A. S. Fokas, B. Pelloni
We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method…
Boundary value problems for the stationary axisymmetric Einstein equations: a rotating disk
J. Lenells, A. S. Fokas
The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst equation, is an integrable nonlinear PDE in two dimensions. There now exists a general…
An integrable generalization of the sine-Gordon equation on the half-line
Jonatan Lenells
We analyze a generalization of the sine-Gordon equation in laboratory coordinates on the half-line. Using the Fokas transform method for the analysis of initial-boundary value prob…
Integrable evolution equations on spaces of tensor densities and their peakon solutions
Jonatan Lenells, Gerard Misiołek, Feride Tiğlay
We study a family of equations defined on the space of tensor densities of weight on the circle and introduce two integrable PDE. One of the equations turns out to be closely r…
Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
Tudor Dimofte, Sergei Gukov, Jonatan Lenells +1
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In th…