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Long-time asymptotics of the good Boussinesq equation and its modified version: Painlevé region
Under suitable solitonless assumptions on the associated scattering data, we rigorously establish the long-time asymptotics of the modified Boussinesq equation in the Painlevé region and its adjacent transition regions for initial data in a weighted Sobolev space. Using the $\dbar$-steepest descent
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