Orbital Stability of Numerical Periodic Nonlinear Schroedinger Equation

J. P. BORGNA, D. RIAL

COMMUNICATIONS IN MATHEMATICAL SCIENCES

INT PRESS BOSTON, INC

Año: 2008 vol. 6 p. 149 - 169

1539-6746

This work is devoted to the study of the system that arises by discretization of the periodic nonlinear Schroedinger equation in dimension one. We study the existence of the discrete ground states for this system and their stability property when the potential parameter 3/4 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.