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111.
A new C-type subhierarchy for KP hierarchy with two new time series γn and σk ((γn,σk)-CKPH), which consists of γn-flow,σk-flow and mixed γn and σkevolution equations of eigenfunctions, is proposed. The zero-curvature representation for the (γn,σk)-CKPH is derived. The reduction and constrained flows of (γn,σk)-CKPH are studied. 相似文献
112.
In this paper, we mainly study three types of gauge transformation operators for the q-mKP hierarchy. The successive applications of these gauge transformation operators are derived. And the corresponding communities between them are also investigated. 相似文献
113.
We study the additional symmetries associated with the q-deformed Kadomtsev–Petviashvili (q-KP) hierarchy. After identifying the resolvent operator as the generator of the additional symmetries, the q-KP hierarchy can be consistently reduced to the so-called q-deformed constrained KP (q-cKP) hierarchy. We then show that the additional symmetries acting on the wave function can be viewed as infinitesimal Bäcklund transformations by acting the vertex operator on the tau-function of the q-KP hierarchy. This establishes the Adler–Shiota–van Moerbeke formula for the q-KP hierarchy. 相似文献
114.
Romesh K Kaul 《Pramana》1982,19(2):183-188
Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry
are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales
under perturbative effects. 相似文献
115.
In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2N − m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations. 相似文献
116.
Ichiro Tsuda Hiroshi Watanabe Hiromichi Tsukada Yutaka Yamaguti 《Entropy (Basel, Switzerland)》2022,24(2)
The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation. 相似文献
117.
讨论了四对谱问题、相应的保谱方程族以及它们Lax表示的等价住,并利用这种等价关系可导出一些方程的Lax表示. 相似文献
118.
XIA Tie-Cheng YU Fa-Jun CHEN Deng-Yuan 《理论物理通讯》2004,42(10)
A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM of the loop algebra G M is presented. Based on FM , the multi-component integrable coupling system of the multi-component C-KdV hierarchy is worked out. The method can be used to other nonlinear evolution equations hierarchy. 相似文献
119.
Fukui Guo Yufeng Zhang Qingyou Yan 《International Journal of Theoretical Physics》2004,43(4):1139-1146
A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra
is constructed, whose commutation operation is clear as that in loop algebra
. Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra
of the loop algebra
is constructed. Taking advantage of
above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out. 相似文献
120.
We show that the BBGKY hierarchy in thermodynamic equilibrium degenerates into an equilibrium hierarchy. In turn, the latter can be used to obtain both the fundamental system of equations describing the state of matter inside a correlation sphere of the radius R10-7cm and the canonical Gibbs distribution, which, according to the current concepts, describes the state of the entire macroscopic system. We show that the Gibbs distribution is indeed also local, i.e., describes the state of matter only inside the correlation sphere; in the thermostat surrounding this sphere, the Gibbs distribution degenerates into a constant. We state that these two approaches are equivalent to each other. 相似文献