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81.
We present integral-type Darboux transformation for the mKdV hierarchy and for the mKdV hierarchy withself-consistent sources. In contrast with the normal Darboux transformation, the integral-type Darboux transformationscan offer non-auto-Backlund transformation between two (2n 1)-th mKdV equations with self-consistent sources withdifferent degrees. This kind of Darboux transformation enables us to construct the N-soliton solution for the mKdVhierarchy with self-consistent sources. We also propose the formulas for the m times repeated integral-type Darbouxtransformations for both mKdV hierarchy and mKdV hierarchy with self-consistent sources. 相似文献
82.
YAN Zhen-Ya 《理论物理通讯》2002,38(10)
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations. 相似文献
83.
Hua Nie Jian-hua Wu 《应用数学学报(英文版)》2006,22(2):257-264
This paper is concerned with the unstirred chemostat model with two-species and one non-reproducingresource.The global attractivity of the positive steady-state solutions of the original system is established.Moreover,the effects of the growth rate on the unique positive equilibrium of the single population model arestudied. 相似文献
84.
Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions. 相似文献
85.
This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort. 相似文献
86.
87.
本文研究作用在C2周期函数空间上的微分算子u→u″ g(u) ,其中g(u)为连续有界函数.我们将证明上述微分算子的值域限制在周期函数空间的“超曲面”中. 相似文献
88.
Piotr Szopa 《Mathematical Methods in the Applied Sciences》2007,30(3):331-346
In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
89.
将散射介质层在z轴方向划分成薄层,用薄层的一阶散射强度、Fourier变换和迭代方法求解散射介质整层的矢量辐射传输(VRT)方程的高阶散射解.该方法将一阶散射与高阶散射迭代结合起来,计算公式简明,可计算高阶迭代解,计算时间少.计算结果与一层均匀散射介质的VRT方程一阶Mueller矩阵解、半空间均匀散射介质二阶Mueller矩阵解、以及离散坐标-特征值特征矢量法的VRT热辐射的数值解作了全面的比较.提出并讨论了非均匀散射层主动与被动VRT方程的高阶解.本计算程序可以通用于非球形粒子多层结构及非均匀介质的散射和热辐射计算.
关键词:
VRT方程
分层
迭代解 相似文献
90.
The effect of the cation concentration, hydrolysis temperature, and composition in the CeO2–ZrO2 system on the direct precipitation of ceria–zirconia solid solutions and the structure of the precipitates from acidic aqueous solutions of (NH4)2Ce(NO3)6 and ZrOCl2 by hydrolysis under hydrothermal conditions were investigated. Nanometer-sized (8–10 nm) ceria–zirconia solid solution particles in a composition range of 0 to 60 mol% ZrO2 were directly precipitated from the solutions with total metal cation concentration less than 0.2 mol/dm3 by simultaneous thermal hydrolysis at 150–240°C. The crystalline phase of the precipitates gradually changed from cubic and/or tetragonal to monoclinic with increasing the cation concentration of the solution from 0.2 to 0.8 mol/dm3 at the starting composition of 50 mol% ZrO2 under hydrolysis condition of 150°C for 48 h, which was attributed to decrease in the supply of hydrolyzed Ce component caused by decrease in the hydrolysis ratio of (NH4)2Ce(NO3)6. Ceria–zirconia solid solutions containing large amount of ZrO2 maintained high specific surface area and small-sized crystallite after heat-treatment at 900–1000°C for 1 h. 相似文献