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Arnold Diffusion of the Discrete Nonlinear Schrödinger Equation

Y. Charles Li
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Abstract

In 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.

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Y. Charles Li. 2006-07-18. Arnold Diffusion of the Discrete Nonlinear Schrödinger Equation. https://arxiv.org/abs/math/0607443

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