Fractional Nonlinear Schr? Dinger Equation For A Long Time State

This paper mainly studies the long-time behavior of solution of the fractional nonlinear Schrodinger equation Which is the standard orthogonal basis, is the imaginary unit,Non-linear Schrodinger equation of quantum mechanics-based mathematical models can be used to describe the light pulses transmission in the dispersion and nonlinear medium, nonlinear optical phenomena and the self-trapped plasma physics Langamui wave, because of its equation in the form of particularity, that is, in general nonlinear evolution equations contain no imaginary number, and many of which we are familiar in the form of nonlinear evolution equations are fundamentally different. Therefore, scholars aroused wide interest. In previous years, there are a number of important conclusions of the long time behavior of solutions for nonlinear Schrodinger equation, but most are directed atαis an integer, whenαis a score ,the long time behavior of these equations has no results. This paper mainly consists of the following five chapters study the long-time behavior of solution of the fractional nonlinear Schrodinger equation:In the first chapter, introduces the physical background and study situation of the Schrodinger equation.In the second chapter, we use the Galerkin method to prove the existence and unique of solutions for such equation.In the third chapter, it is obtained for that the existence of global attractor for such equation.In the fourth chapter, the global attractor dimension is estimated to obtain its Hausdorff dimension and fractal dimension of the upper bound estimate.In the fifth chapter, we discuss the long-time behavior of solution of such equation; an approximate inertial manifold is constructed for such equation.