We survey and compare, mainly in the two-dimensional case, various results obtained by IST and PDE techniques for integrable equations. We also comment on what can be predicted from integrable equations on non integrable ones.
Dispersive Asymptotics for Linear and Integrable Equations by the $\overline{\partial}$ Steepest Descent Method
Time-periodic solutions to the Navier--Stokes equations on the whole space including the two-dimensional case
A Novel Approach to Elastodynamics: I. The Two-Dimensional Case
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