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The hydrological processes are becoming more and more complex. Fractal dimension is one of the important measurements of complexity. This paper utilizes wavelets transform technique to calculate the fractal dimension of rainfall in July for eight stations (Yushu, Xichang, Pingshan, Lijiang, Kunming, Huili, Deqin, Lnage ) in the Jinsha River Basin. The results show: the rainfall series in the Jinsha River Basin is fractal; the approach for estimating the fractal dimension by using wavelet transform coefficients is feasible and effective; the fractal dimension of rainfall reflect the influence of factors on the rainfall.

The dissipative quantum Zakharov equations are mainly studied. The existence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori estimate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated.

In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor Ai in Hi(Ω) is actually equal to a global attractor Aj in Hj(Ω) (i ≠ j, i, j = 1, 2, … m).

The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H 0 1 .

The stochastic dissipative quantum Zakharov equations with white noise are studied. The existence and uniqueness of solutions are obtained by using the standard Galerkin approximation method on the basis of the time uniform a priori estimates in various spaces. Moreover, the asymptotic behaviors of the solutions for the stochastic dissipative quantum Zakharov equations with white noise are also investigated.