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 ...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^1 0.展开更多
Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meant...Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meantime it is shown that this leads to a direct reduction in the form of ordinary differential equation under some integrability conditions between the variable coefficients. Two different cases have been discussed, the search for solutions of those ordinary differential equations yielded many exact travelling and solitonic wave solutions in the form of hyperbolic and trigonometric functions under some constraints between the variable coefficients.展开更多
In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of ...In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.展开更多
基金supported by the National Natural Science Foundation of China (No. 10661002)the NaturalScience Foundation of Guangxi (No. 0832065)the Excellent Talents Fund of Guangxi (No. 0825)
文摘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^1 0.
文摘Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meantime it is shown that this leads to a direct reduction in the form of ordinary differential equation under some integrability conditions between the variable coefficients. Two different cases have been discussed, the search for solutions of those ordinary differential equations yielded many exact travelling and solitonic wave solutions in the form of hyperbolic and trigonometric functions under some constraints between the variable coefficients.
基金This work is supported by National Natural Science Foundation of China under Grant nos, 10001013 and 10471047 and Natural Science Foundation of Guangdong Province of China under Grant no. 004020077.
文摘In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.
