共查询到20条相似文献，搜索用时 15 毫秒
1.
In this paper, the authors define the noncommutative constrainedKadomtsev-Petviashvili (KP) hierarchy and multi-componentnoncommutative constrained KP hierarchy. Then they give therecursion operators for the noncommutative constrained KP (NcKP)hierarchy and multi-component noncommutative constrained KP (NmcKP)hierarchy. The authors hope these studies might be useful in thestudy of D-brane dynamics whose noncommutative coordinates emergefrom limits of the M theory and string theory. 相似文献
2.
The dispersionless Kadomtsev–Petviashvili hierarchy is generalized by introducing two new time series γn and σk with two parameters ηn and λk. By this hierarchy, we obtain the first type, the second type as well as mixed type of dispersionless Kadomtsev–Petviashvili equation with self‐consistent sources and their related conservation equations. In addition, the reduction and constrained flow of this new hierarchy are studied. The first type, the second type and the mixed type of dispersionless Korteweg–de Vries equation with self‐consistent sources and of dispersionless Boussinesq equation with self‐consistent sources are obtained. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
3.
首先讨论了约束离散KP可积方程族一种等价形式:差分算子的商.接下来,利用这种新的描述形式,构造了约束离散KP方程族的完全Virasoro对称. 相似文献
4.
Kadomstev-Petviashvili(KP)系列的r-函数能够表示成生成函数的广义Wronskian行列式,这里的生成函数满足一组线性偏微分方程.本文引入一种新的方法把由规范变换Tn+k生成的KP系列约化到M(相似文献
5.
The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction {Φ i , Ψ i } are presented explicitly. Furthermore, we show that acting on the space of the wave operator, *k forms new centerless W cC 1+∞ and W cB 1+∞ -subalgebra of centerless W 1+∞ respectively. In order to define above symmetry flows *k of the cCKP and cBKP hierarchies, two vital operators Y k are introduce... 相似文献
6.
Yi Zhang Haifeng Huo Yinkang Xu Yinjie Lu 《Journal of Nonlinear Modeling and Analysis》2019,1(2):179-192
By virtue of the KP hierarchy reduction method, the N-dark soli-ton solutions of the multi-component Maccari system are constructed. Takingthe coupled Maccari system for instance, the N-dark soliton solutions are fur-ther obtained in terms of determinants. In addition, in contrast with bright-bright soliton collisions, the dynamical analysis shows that the collisions ofdark-dark solitons are elastic and there is no energy exchange among soli-tons in different components. What’s more, we also investigate the dark-darksoliton bound states including stationary and moving ones. 相似文献
7.
《Integral Transforms and Special Functions》2012,23(6):517-527
A recursion relation of hyperelliptic ψ functions of genus two, which was derived by D. G. Cantor (J. reine angew. Math. 447 (1994) 91–145), is studied. As Cantor's approach is algebraic, another derivation is presented as a natural extension of the analytic derivation of the recursion relation of the elliptic ψ function in a sense of study of special functions. 相似文献
8.
The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the au-thors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given. 相似文献
9.
本文从约化的角度考虑BKP方程族的Pfaffian形式的解.证明了通过施加适当的微分约束,KP方程族的格拉姆行列式的解很自然的约化为BKP方程族的解. 相似文献
10.
该文讨论了KP和mKP可积系列及其约束情形的平方本征对称与Miura变换和反-Miura变换的关系. 相似文献
11.
本文讨论的是ＫＰ系统Ｌａｘ算子及主对称的换位公式．通过拓广速降函数空间及对 ＫＰ方程 Ｌａｘ算子的讨论,找到了 Ｌａｘ算子的表示向量;并通过对 Ｌａｘ算子、 Ｌａｘ流、 Ｌａｘ算子表示向量之间联系的讨论,得出了计算 Ｌａｘ算子李括号的表示向量的方法,从而解决了 ＫＰ方程主对称的换位公式问题．最后本文还利用伴随算子给出了从ＫＰ方程任一主对称得到其一个对称的公式． 相似文献
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14.
S. M. Natanzon 《Functional Analysis and Its Applications》2003,37(1):21-31
We derive formulas making it possible to calculate the Taylor expansion coefficients of the string solution for the Gelfand–Dikii hierarchy. According to the Witten conjecture, these coefficients coincide with the Mumford–Morita–Miller intersection numbers (correlators) of stable cohomology classes for the moduli space of n-spin bundles on Riemann surfaces with punctures. 相似文献
15.
The iterated Darboux transformations of an ordinary differential operator are constructively parametrized by an infinite-dimensional Grassmannian of finitely supported distributions. In the case that the operator depends on time parameters so that it is a solution to the n-KdV hierarchy, it is shown that the transformation produces a solution of the KP hierarchy. The standard definitions of the theory of -functions are applied to this Grassmannian and it is shown that these new -functions are quotients of KP -functions. The application of this procedure for the construction of higher rank KP solutions is discussed. 相似文献
16.
In this letter, we investigate the dynamics and various interaction scenarios of localized wave structures in the Kadomtsev–Petviashvili (KP)-based system. By using a combination of the Hirota’s bilinear method and the KP hierarchy reduction method, new families of determinant semi-rational solutions of the KP-based system are derived, including lump solitons and rogue-wave solitons. The generic interaction scenarios between distinct types of localized wave solutions are investigated. Our detailed study reveals different types of interaction phenomena: fusion of lumps and line solitons into line solitons, fission of line solitons into lumps and line solitons, a mixture of fission and fusion processes of lumps and line solitons, and the inelastic collision of line rogue waves and line solitons. 相似文献
17.
Andr Nies 《Mathematical Logic Quarterly》1994,40(4):490-518
We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th(Eq*) has the same computational complexity as the true first-order arithmetic. Mathematics Subject Classification: 03D25, 03D15, 03D35. 相似文献
18.
M. Kazarian 《Advances in Mathematics》2009,221(1):1-21
Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's λg-conjecture, etc. Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy. 相似文献
19.
We use the BBGKY hierarchy and the mass, momentum, and intrinsic energy conservation laws, which are consequences of this hierarchy, to obtain the hydrodynamic equations for multicomponent systems and the diffusion equations. We formulate several restrictions on the thermodynamic equations for irreversible processes. 相似文献
20.
In this paper, the Maccari system is investigated, which is viewed as a two-dimensional extension of nonlinear Schrödinger equation. We derive doubly localized two-dimensional rogue waves on the dark solitons of the Maccari system with Kadomtsev–Petviashvili hierarchy reduction method. The two-dimensional rogue waves include line segment rogue waves and rogue-lump waves, which are localized in two-dimensional space and time. These rogue waves are generated by the resonant collision of rational solitary waves and dark solitons, the whole process of transforming elastic collision into resonant collision is analytically studied. Furthermore, we also discuss the local characteristics and asymptotic properties of these rogue waves. Simultaneously, the generating conditions of the line segment rogue wave and rogue-lump wave are also given, which provides the possibility to predict rogue wave. Finally, a new way to obtain the high-order rogue waves of the nonlinear Schrödinger equation are given by proper reduction from the semi-rational solutions of the Maccari system. 相似文献