Schrödinger方程不仅是量子力学的基础方程之一, 也是偏微分方程中一个重要的方程.. 拟线性Schrödinger型方程是等离子体、非线性光学等物理领域中的重要模型，也是一类重要的色散方程。本项目拟应用调和分析、泛函分析、算子的谱理论研究拟线性Schrödinger型方程孤立波解的稳定性理论。主要包括：.1.拟运用规范形式（normal forms）理论和算子的谱理论，研究带位势Schrödinger方程初值在基态与激发态之间时解的长时间行为。.2.拟运用变分理论和调制稳定性理论，研究广义导数Schrödinger方程孤立波解的强不稳定性以及爆破解的存在性。.3.拟运用退化性质和维里量泛函理论，研究带五次非线性项的导数Schrödinger方程孤立波解在退化情形时的不稳定性。

Schrödinger equation is an important equation of partial differential equation and plays an fundamental role in the quantum mechanics equation..The quasilinear Schrödinger equations are important models in plasma physics, nonlinear optics, and so on. In this project, we are going to apply the theories of harmonic analysis, functional analysis and the spectral analysis of operators, to study stability theory of solitary wave solutions for the quasilinear Schrödinger equations. The project will mainly discuss several problems as following: .1..We will study the long time behavior of the solution for initial data near ground states or excited states for the nonlinear Schrödinger equations with potential, by using the tools of normal forms and the spectral analysis of operators..2..We are going to study the strong instability and the existence of blow-up solution for the generalized derivative nonlinear Schrödinger equations by using the theories of variation and modulation. .3..We will consider to study the instability of the solitary wave solutions for the derivative nonlinear Schrödinger equations in the degenerate case. We will use the degenerate condition and the theories of virial functions.