Open Access
March 2008 Orbital stability of numerical periodi nonlinear Schrödinger equation
Juan P. Borgna, Diego F. Rial
Commun. Math. Sci. 6(1): 149-169 (March 2008).


This work is devoted to the study of the system that arises by discretization of the periodic nonlinear Schrödinger equation in dimension one. We study the existence of the discrete ground states for this system and their stability property when the potential parameter ¾ is small enough: i.e., if the initial data are close to the ground state, the solution of the system will remain near to the orbit of the discrete ground state forever. This stability property is an appropriate tool for proving the convergence of the numerical method.


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Juan P. Borgna. Diego F. Rial. "Orbital stability of numerical periodi nonlinear Schrödinger equation." Commun. Math. Sci. 6 (1) 149 - 169, March 2008.


Published: March 2008
First available in Project Euclid: 7 March 2008

zbMATH: 1155.65069

Primary: 34L15 , 35J25 , 35P30

Keywords: Ground states , numerical periodic nonlinear Schrödinger equation , orbital stability

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 1 • March 2008
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