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Existence and equicontinuity of solutions to the Kirchhoff--Pohozaev wave equation
Luccas Campos, Rowan Killip, Monica Visan
It was recently discovered by Boiti--Manfrin that a variant of the Kirchhoff wave equation introduced by Pohozaev admits infinitely many conserved quantities. In this paper, we obt…
Scattering and nonlinear recovery for the 1 NLW with localized nonlinearity
Luccas Campos, Jason Murphy, Renzo Scarpelli
We consider the wave equation in 1 with a spatially-localized cubic nonlinearity. We establish scattering in a weighted space and demonstrate the injectivity of the scattering m…
Threshold dynamics for the radial cubic NLS with repulsive inverse-square potential
Luke Baker, Luccas Campos, Jason Murphy +1
We classify the dynamics of radial solutions at the (radial) ground state threshold for the cubic NLS in the presence of a repulsive inverse-square potential.
Determination of radial nonlocal nonlinearities from the scattering map
Luccas Campos, Rowan Killip, Jason Murphy +1
We show that the small-data scattering map uniquely determines the nonlinearity for a class of nonlinear Schrödinger equations with radial, Hartree-type nonlinearities. Our assumpt…
Large data scattering for the defocusing -dispersion generalized Benjamin-Ono equation in the energy space
Luccas Campos, Felipe Linares, Thyago S. R. Santos
We study the defocusing -dispersion generalized Benjamin-Ono equation. For every even integer , we prove that solutions with initial data in the energy space $H^{\fracα…
Threshold solutions for the cubic INLS: the energy-critical case
Luccas Campos, Luiz Gustavo Farah, Jason Murphy
We study the energy-critical cubic inhomogeneous NLS equation . In this work, we prove the existence of special solutions with…