2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115032In this article, we prove the existence of Arnold diffusion for an interesting specific system -- discrete nonlinear Schrödinger equation. The proof is for the 5-dimensional case with or without resonance. In higher dimensions, the problem is open. Progresses are made by establishing a complete set of Melnikov-Arnold integrals in higher and infinite dimensions. The openness lies at the concrete computation of these Melnikov-Arnold integrals. New machineries introduced here into the topic of Arnold diffusion are the Darboux transformation and isospectral theory of integrable systems.24ppDynamical SystemsMathematical PhysicsAnalysis of PDEsChaotic Dynamics37, 34, 35, 78, 76text