11 papers
Decay and regularity properties for the dispersion generalized Benjamin-Ono equation
Germán Fonseca, Oscar Riaño, Guillermo Rodríguez-Blanco
We study spatial decay properties of solutions to the dispersion generalized Benjamin-Ono equation. We first establish persistence properties in weighted Sobolev spaces under a sha…
On Kato's smoothing effects for KdV and Benjamin type equations
Carlos Garzón, Oscar Riaño
We analyze how the interaction between local and nonlocal dispersions, combined with different types of nonlinearities, influences the smoothing effects of solutions. To achieve th…
The nonlinear Schrödinger equation with combined nonlinearities in 1D
Oscar Riaño, Oscar Riaño, Alex D Rodriguez +1
We consider the one-dimensional nonlinear Schrödinger equation with the nonlinearity term that is expressed as a s…
A monotonicity formula for the fractional Laplacian and instability results for the Shrira equation
Argenis J. Méndez, Oscar Riaño
By employing a new class of pseudo-differential operators introduced in a previous work, we establish a novel monotonicity formula for the fractional Laplacian in $…
Existence and uniqueness of radial solutions of semi-linear equations on manifolds
Nicolas Martinez-Alba, Oscar Riaño
We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold . By combining differential…
On the decay of solutions for the negative fractional KdV equation
Alysson Cunha, Oscar Riaño, Ademir Pastor
We explore the limits of fractional dispersive effects and their incidence in the propagation of polynomial weights. More precisely, we consider the fractional KdV equation when a…