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Alex H. Ardila

Publications and source records attributed to Alex H. Ardila.

21 records · Page 2Linked to original sources
arXiv2017

Logarithmic NLS equation on star graphs: existence and stability of standing waves

In this paper we consider the logarithmic Schrödinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. Then we show the existence of several families of standing waves. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we show that the ground states are orbitally stable via a variational approach.

math.AP↗
arXiv2017

Orbital stability of standing waves for a system of nonlinear Schrödinger equations with three wave interaction

We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schrödinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a characterization of the standing waves solutions as minimizers of an energy functional subject to three independent $L^{2}$ mass constraints. As a consequence, we establish existence and orbital stability of solitary waves.

math.AP↗