Jaime Angulo

Global well-posedness and non-linear stability of periodic traveling wavesfor a Schrödinger-Benjamin-Ono system

Published in Communications on Pure & Applied Analysis

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases...

Stability properties of periodic traveling waves for the Intermediate Long Wave Equation

In this paper, we determine orbital and linear stability of periodic waves with the mean zero property related to the Intermediate Long Wave equation. Our arguments follow the recent developments in andrade-pastor, natali and DK to deduce the orbital/linear stability of periodic traveling waves.

The Non-Linear Schrödinger Equation with a periodic 𝛅--interaction

We study the existence and stability of the standing waves for the periodic cubic nonlinear Schrödinger equation with a point defect determined by a periodic Dirac distribution at the origin. This equation admits a smooth curve of positive periodic solutions in the form of standing waves with a profile given by the Jacobi elliptic function of dnoid...

Nonlinear Stability for the Periodic and Non-Periodic Zakharov System

We prove the existence of a smooth curve of periodic traveling wave solutions for the Zakharov system. We also show that this type of solutions are nonlinear stable by the periodic flow generated for the system mentioned before. An improvement of the work of Ya Ping is made, we prove the stability of the solitary wave solutions associated to the Za...