上世纪60年代以来创立的KAM理论、Nekhoroshev估计(长时间稳定)以及Arnold扩散理论能够较为清楚地描绘有限维近可积哈密顿系统的动力学行为。把上述三种理论推广到由偏微分方程定义的无穷维Hamilton系统上，是相对较新的课题，有大量悬而未决的问题。近二十多年来，在对具有有界扰动的非线性偏微分方程定义的无穷维哈密顿系统的KAM理论、长时间稳定的研究已取得了长足的进步，但对有无界扰动的偏微分方程的KAM理论、长时间稳定、Arnold扩散的研究很少或几乎没有。我们计划研究具无界扰动的偏微分方程（特别是高空间维数的方程如KP-方程、带导数的非线性薛定谔方程）等的KAM理论、长时间稳定性和Arnold扩散（即不稳定性）。

Since 1960's, KAM theory and Nekhoroshev estimate(long time stability) and the theory on Arnold diffusion have been established to depict the dynamical behaviours of the nearly integrable Hamiltonian systems of finite dimension.It is a relatively new topics to extend those theories to the infinite dimensional Hamiltonian systems defined by partial differential equations, and there are many open problems.In recent 20 years, a large progress has been achieved on the KAM theory and long stability for the infinite dimensional Hamiltonian systems defined by partial differential equations of bounded perturbation. However, there are few progresses for the partial differentail equations of unbounded perturbation. We are planning in this propose to investigate KAM theory and long time stability and Arnold diffusion for the partial differential equations of unbounded perturbation, especially for KP-equation and the derivative nonlinear Schroedinger equations of higher spatial dimension.