The Global Soutions Of The Cauchy Problem For One Class Schr(?)dinger Type Equations

Nonlinear Schrodinger type equations come from quantum mechanics, nonlinear optical, electromagnetic, plasma theory, solid-state physics and other modern physics research. In recent years, many mathematic researchers are interested in the Cauchy problems for these equations, but there are many problems which haven't been solved completely. In this paper we study some Schrodinger type equations and coupled Schrodinger equations. By Banach fixed point theorem, the global solutions are obtained. This paper is divided into three chapters.In the first chapter, we briefly introduce the research questions and research status. The main works are presented in this paper, and we introduce the basic concepts.In the second chapter, we study the anisotropic sixth-order and 2m-order Schrodinger equations. By Banach fixed point theorem, the global small solutions are obtained in one measurable space.In the third chapter, we study the global solutions of one class coupled Schrodinger equations in Sobolev Space.