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math.AP2025
Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations
Simão Correia, Gonçalo Pereira, Thyago S. R. Santos
Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction…
math.AP2025
Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation
Simão Correia, Shinya Kinoshita
We consider the Cauchy problem associated with the modified Zakharov-Kuznetsov equation over . Taking into consideration the associated dispersive effects, we introdu…
math.AP2025
Nonlinear smoothing implies improved lower bounds on the radius of spatial analyticity for nonlinear dispersive equations
Mikaela Baldasso, Simão Correia
We provide a roadmap to establish improved lower bounds on the decay rate of the uniform radius of analyticity for a given nonlinear dispersive equation, reducing the proble…