Global Attractor for a Generalized Discrete Nonlinear Schrdinger Equation
A generalized discrete nonlinear Schrdinger equation $$i\dot{u}_n(t)+\sum_{m=-\infty}^{+\infty} J(n-m)u_m(t)+g\bigl(u_n(t)\bigr)+i\gamma u_n(t)=f_n,\quad n\in\mathbb{Z}, $$ with long-range interactions in weighted spaces \(\ell_{\mathbf{{q}}}^{2}\) is considered. Under suitable assumptions on the coupling constants J(m), the damping ? and the weight \(\mathbf{{q}}=(q_{n})_{n\in \mathbb{Z}}\), the existence of a global attractor is proved.
global attractor discrete nonlinear schrdinger equation long-range interactions localized solutions 5q55 34k30 35b41