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作者在三维全空间中考虑研究复Ginzburg Landau方程(CGL)的解的长时间行为。通过引入权空间,应用内插不等式和在权空间的先验估计,获得复 Ginzburg Landau方程整体解的存在性,进一步建立了整体吸引子的存在性。 相似文献
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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. 相似文献
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考虑带附加噪声的随机广义2D Ginzburg-Landau方程.通过先验估计的方法,随机动力系统的紧性得到证明,进一步验证了该随机动力系统在础存在随机整体吸引子. 相似文献
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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. 相似文献
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The spatial-temporal bifurcation for Kadomtsev-Petviashvili (KP) equations is considered. Exact two-soliton solution and doubly periodic solution to the KP-I equation, and two classes of periodic soliton solutions in different directions to KP-Ⅱ are obtained using the bilinear form, homoclinic test technique and temporal and 1 spatial transformation method, respectively. The equilibrium solution uo =-1/6, a unique spatial-temporal bifurcation which is periodic bifurcation for KP-I and deflexion of soliton for KP-Ⅱ, is investigated. 相似文献
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Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated. 相似文献
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The exact periodic homoclinic wave of (1+1)D long-short wave equation is obtained using an extended homoclinic test technique. This result shows complexity and variety of dynamical behaviour for a (1+1)-dimensional long-short wave equation. 相似文献
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A new technique, the extended homoclinic test technique, is proposed to seek periodic solitary wave solutions of integrable systems. Exact periodic solitary-wave solutions for classical KdV equation are obtained using this technique. This result shows that it is entirely possible for the (l + l)-dimensional integrable equation that there exists a periodic solitary-wave. 相似文献