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991.
Ravi P. Agarwal 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):2859-124
We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented. 相似文献
992.
The application of quantum dots in advanced technology goes beyond doubt. Here, based on an analytical methodology, investigate a three-electron-quantum dot in the presence of Rashba spin–orbit interaction under cylindrical symmetry. Both eigenvalues and eigenfunctions of the system are reported and the problem is numerically discussed. 相似文献
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We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|2σu. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ+1<3.68; bistability, in a finite range of values of the soliton’s power, for 3.68<2σ+1<5; and the presence of a threshold (minimum norm of the FS), for 2σ+1≥5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely. 相似文献
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This note studies the iterative solutions to the coupled Sylvester-transpose matrix equation with a unique solution. By using the hierarchical identification principle, an iterative algorithm is presented for solving this class of coupled matrix equations. It is proved that the iterative solution consistently converges to the exact solution for any initial values. Meanwhile, sufficient conditions are derived to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Finally, a numerical example is given to illustrate the efficiency of the proposed approach. 相似文献
1000.