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151.
Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some (2+1)- dimensional nonlinear Schrodinger-like equations are constructed based on Hirota's bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel'nikov equation, and g-Schrodinger equation are constructed based on Hirota's bilinear method. 相似文献
152.
The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions (including kinky periodic solitary-wave solutions, periodic soliton solutions, and crosskink-wave solutions) for the new (2+1)-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field. 相似文献
153.
The present paper concentrates on the analogues of Rosenthal's inequalities for ordinary and decoupled bilinear forms in symmetric random variables. More specifically, we prove the exact moment inequalities for these objects in terms of moments of their individual components. As a corollary of these results we obtain the explicit expressions for the best constant in the analogues of Rosenthal's inequality for ordinary and decoupled bilinear forms in identically distributed symmetric random variables in the case of the fixed number of random variables. 相似文献
154.
The optimization problem with the Bilinear Matrix Inequality (BMI) is one of the problems which have greatly interested researchers of system and control theory in the last few years. This inequality permits to reduce in an elegant way various problems of robust control into its form. However, in contrast to the Linear Matrix Inequality (LMI), which can be solved by interior-point-methods, the BMI is a computationally difficult object in theory and in practice. This article improves the branch-and-bound algorithm of Goh, Safonov and Papavassilopoulos (Journal of Global Optimization, vol. 7, pp. 365–380, 1995) by applying a better convex relaxation of the BMI Eigenvalue Problem (BMIEP), and proposes new Branch-and-Bound and Branch-and-Cut Algorithms. Numerical experiments were conducted in a systematic way over randomly generated problems, and they show the robustness and the efficiency of the proposed algorithms. 相似文献
155.
The nature of the base pairing between cytosine and 2‐aminopurine is investigated by means of quantum mechanical calculations including electron correlation and accounting for the effects of aqueous solvation. At neutral pH, both a neutral wobble base pair and a Watson–Crick‐like base pair having a protonated 2‐aminopurine are predicted to be close to one another in energy; other previously proposed forms are found to be too high in energy to be of significant chemical interest. Accounting for the energetics of helix embedding suggests that the equilibrium between the two low‐energy motifs is quite sensitive to local environment. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1167–1179, 2001 相似文献
156.
This paper derives some optimization results for bilinear systems using a higher-order method by characterizing them over matrix Lie groups. In the derivation of the results, first a bilinear system is transformed to a left-invariant system on matrix Lie groups. Then, the product of exponential representation is used to express this system in canonical form. Next, the conditions for optimality are obtained by the principles of variational calculus. It is demonstrated that closed-form analytical solutions exist for classes of bilinear systems whose Lie algebra are nilpotent. 相似文献
157.
ZHANG Yuan-Yuan WANG Qi ZHANG Hong-Qing 《理论物理通讯》2007,48(3):411-414
In this paper, negatons, positons, and complexiton solutions of higher order for a non-isospectral KdV equation, the KdV equation with loss and non-uniformity terms are obtained through the bilinear Baicklund transformation. Further, the properties of some solutions are shown by some figures made by using Maple. 相似文献
158.
描述大形变核中对力的硬核Bose-Hubbard模型 总被引:3,自引:0,他引:3
讨论了一种描述大形变偶偶核邻近轨道对力相互作用近似的硬核Bose-Hubbard模型.利用代数方法得到了该模型对激发谱和相应波函数的严格解.该结果可推广到具有任意自旋和有限格点的硬核Bose-Hubbard和Fermi-Hub-bard模型中去. 相似文献
159.
Higher-Dimensional KdV Equations and Their Soliton Solutions 总被引:2,自引:0,他引:2
A (2+1)-dimensional KdV equation is obtained by use of Hirota
method, which possesses N-soliton solution, specially its exact
two-soliton solution is presented. By employing a proper algebraic
transformation and the Riccati equation, a type of bell-shape
soliton solutions are produced via regarding the variable in the
Riccati equation as the independent variable. Finally, we extend
the above (2+1)-dimensional KdV equation into (3+1)-dimensional
equation, the two-soliton solutions are given. 相似文献
160.
Soliton solution and interaction property for a coupled modified Korteweg-de Vries (mKdV) system
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Hirota's bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries (mKdV) system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this (1+1)-dimensional integrable coupled model. 相似文献