7 papers
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 assump…
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^{\fracÎ…
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…
Threshold solutions for the cubic INLS: the energy-subcritical case
Luccas Campos, Luiz Gustavo Farah, Jason Murphy
We revisit the work [L. Campos and J. Murphy, SIAM J. Math. Anal., 55 (2023), pp. 3807--3843], which classified the dynamics of solutions at the ground state threshold for cu…