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Pedro Isaza

Publications and source records attributed to Pedro Isaza.

7 recordsLinked to original sources
arXiv2015

On the propagation of regularity of solutions of the Kadomtsev-Petviashvilli (KPII) equation

We shall deduce some special regularity properties of solutions to the IVP associated to the KPII equation. Mainly, for datum $u_0\in X_s(\mathbb R^2)$, $s>2$, (see (1.2) below) whose restriction belongs to $H^m((x_0,\infty)\times\mathbb R)$ for some $m\in\mathbb Z^+,\,m\geq 3,$ and $x_0\in \mathbb R$, we shall prove that the restriction of the corresponding solution $u(\cdot,t)$ belongs to $H^m((β,\infty)\times\mathbb R)$ for any $β\in \mathbb R$ and any $t>0$.

math.AP↗
arXiv2014

On the propagation of regularities in solutions of the Benjamin-Ono equation

We shall deduce some special regularity properties of solutions to the IVP associated to the Benjamin-Ono equation. Mainly, for datum $u_0\in H^{3/2}(\mathbb R)$ whose restriction belongs to $H^m((b,\infty))$ for some $m\in\mathbb Z^+,\,m\geq 2,$ and $b\in \mathbb R$ we shall prove that the restriction of the corresponding solution $u(\cdot,t)$ belongs to $H^m((β,\infty))$ for any $β\in \mathbb R$ and any $t>0$. Therefore, this type of regularity of the datum travels with infinite speed to its left as time evolves.

math.AP↗
arXiv2014

Propagation of regularity and decay of solutions to the $k$-generalized Korteweg-de Vries equation

We study special regularity and decay properties of solutions to the IVP associated to the $k$-generalized KdV equations. In particular, for datum $u_0\in H^{3/4^+}(\mathbb R)$ whose restriction belongs to $H^l((b,\infty))$ for some $l\in\mathbb Z^+$ and $b\in \mathbb R$ we prove that the restriction of the corresponding solution $u(\cdot,t)$ belongs to $H^l((β,\infty))$ for any $β\in \mathbb R$ and any $t\in (0,T)$. Thus, this type of regularity propagates with infinite speed to its left as time evolves.

math.AP↗
arXiv2014

Decay properties for solutions of fifth order nonlinear dispersive equations

We consider the initial value problem associated to a large class of fifth order nonlinear dispersive equations. This class includes several models arising in the study of different physical phenomena. Our aim is to establish special (space) decay properties of solutions to these systems. These properties complement previous unique continuation results and in some case, show that they are optimal. These decay estimates reflect the "parabolic character" of these dispersive models in exponential weighted spaces. This principle was first obtained by T. Kato in solutions of the KdV equation

math.AP↗
arXiv2013

Unique continuation principle for high order equations of Korteweg-de Vries type

In this article we consider the problem of unique continuation for a class of high order equations of Korteweg-de Vries type which include the kdV hierachy. It is proved that if the difference w of two solutions of an equation of this form has certain exponential decay for x>0 at two different times, then w is identically zero.

math.AP↗
arXiv2012

On decay properties of solutions of the $k$-generalized KdV equations

We prove special decay properties of solutions to the initial value problem associated to the $k$-generalized Korteweg-de Vries equation. These are related with persistence properties of the solution flow in weighted Sobolev spaces and with sharp unique continuation properties of solutions to this equation. As application of our method we also obtain results concerning the decay behavior of perturbations of the traveling wave solutions as well as results for solutions corresponding to special data.

math.AP↗