共查询到20条相似文献,搜索用时 15 毫秒
1.
《理论物理通讯》2015,(10)
In this paper, we derive the bi-Hamiltonian structure of a multi-component Camassa–Holm system, which associates with the multi-component AKNS hierarchy and multi-component KN hierarchy via the tri-Hamiltonian duality method. Furthermore, the spectral problems of the dual hierarchies may be obtained. 相似文献
2.
3.
It is observed that the Camassa–Holm equation describes pseudo-spherical surfaces and that therefore, its integrability properties can be studied by geometrical means. An sl(2, R)-valued linear problem whose integrability condition is the Camassa–Holm equation is presented, a Miura transform and a modified Camassa–Holm equation are introduced, and conservation laws for the Camassa–Holm equation are then directly constructed. Finally, it is pointed out that this equation possesses a nonlocal symmetry, and its flow is explicitly computed. 相似文献
4.
We propose and develop another approach to constructing multi-soliton solutions of an integrable two-component Camassa–Holm(CH2)system.With the help of a reciprocal transformation and a gauge transformation,we relate the CH2 system to a negative flow of the Broer–Kaup or twoboson hierarchy.The solutions of this negative flow are given in terms of Wronskians via Darboux transformation.Then the multi-soliton solutions of the CH2 system are recovered in parametric form by inverting the reciprocal transformation and the gauge transformation. 相似文献
5.
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of
endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation. 相似文献
6.
In this paper, we study an integrable generalization of the associated Camassa–Holm equation. The generalized system is shown to be integrable in the sense of Lax pair and the bilinear Bäcklund transformations are presented through the Bell polynomial technique. Meanwhile, its infinite conservation laws are constructed, and conserved densities and fluxes are given in explicit recursion formulas. Furthermore, a Darboux transformation for the system is derived with the help of the gauge transformation between two Lax pairs. As an application, soliton and periodic wave solutions are given through the Darboux transformation. 相似文献
7.
8.
Guilong Gui Yue Liu Peter J. Olver Changzheng Qu 《Communications in Mathematical Physics》2013,319(3):731-759
In this paper, we investigate the formation of singularities and the existence of peaked traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The equation is known to be integrable, and is shown to admit a single peaked soliton and multi-peakon solutions, of a different character than those of the Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and a new wave-breaking mechanism for solutions with certain initial profiles is described in detail. 相似文献
9.
In a number of scaling limits, we prove estimates relating the solutions of the Camassa–Holm equation to the solutions of the associated KdV equation. As a consequence, suitable solutions of the water wave problem and solutions of the Camassa–Holm equation stay close together for long times. 相似文献
10.
Utilizing some conservation laws of the(1+1)-dimensional Camassa–Holm(CH) equation and/or its reciprocal forms, some(n+1)-dimensional CH equations for n ≥ 1 are constructed by a modified deformation algorithm.The Lax integrability can be proven by applying the same deformation algorithm to the Lax pair of the(1+1)-dimensional CH equation. A novel type of peakon solution is implicitly given and expressed by the Lambert W function. 相似文献
12.
《理论物理通讯》2016,(12)
This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity. 相似文献
13.
14.
15.
We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa–Holm equation. Utilizing the solution of the indefinite moment problem given by M. G. Krein and H. Langer, we show that the conservative Camassa–Holm equation is integrable by the inverse spectral transform in the multi-peakon case. 相似文献
16.
In this paper a two-step iterative solution algorithm for solving the Camassa–Holm equation, which involves only the first-order derivative term, is presented. In each set of the u − P and u − m differential equations, one is governed by the inviscid nonlinear convection–reaction equation for the time-evolving fluid velocity component along the horizontal direction. The other equation is known as the inhomogeneous Helmholtz equation. The resulting reduction of differential order facilitates us to develop the flux discretization scheme in a stencil with comparatively fewer points. For accurately predicting the unidirectional propagation of the shallow water wave, the modified equation analysis for eliminating several leading discretization error terms and the Fourier analysis for minimizing a particular type of wave-like error are employed. In this study, the fifth-order spatially accurate combined compact upwind scheme is developed in a three-point stencil for approximating the first-order derivative term. For the purpose of retaining a long-term accurate Hamiltonian and multi-symplectic geometric structures in Camassa–Holm equation, the time integrator (or time-stepping scheme) chosen in this study should conserve symplecticity. Another main emphasis of conducting the present calculation of Camassa–Holm equation is to shed light on the conservation of Hamiltonians up to the time before wave breaking. We also intended to elucidate the switching scenario by virtue of the peakon–peakon interaction problem and the dissipative scenario after the time of head-on collision in the peakon–antipeakon interaction problem. 相似文献
17.
A semiclassical theory of a dissipative Henon—Heiles system is proposed. Based on -scaling of an equation for the evolution of the Wigner quasiprobability distribution function in the presence of dissipation and thermal diffusion, we derive a semiclassical equation for quantum fluctuations, governed by the dissipation and the curvature of the classical potential. We show how the initial quantum noise gets amplified by classical chaotic diffusion, which is expressible in terms of a correlation of stochastic fluctuations of the curvature of the potential due to classical chaos, and ultimately settles down to equilibrium under the influence of dissipation. We also establish that there exists a critical limit to the expansion of phase space. The limit is set by chaotic diffusion and dissipation. Our semiclassical analysis is corroborated by numerical simulation of a quantum operator master equation. 相似文献
18.
Perturbation differential equations of motion of a general nonholonomic system subjected to the ideal nonholonomic constraints of Chetaev's type are established, and the equation of variation of energy is deduced by using the perturbation equations of the system. A criterion of the stability is obtained and an example is given to illustrate the application of the result. 相似文献
19.
GUO Fu-Kui 《理论物理通讯》2007,48(5):769-772
A general Lie algebra Vs and the corresponding loop algebra Vx are constructed, from which the linear isospectral Lax pairs are established, whose compatibility presents the zero curvature equation. As its application, a new Lax integrable hierarchy containing two parameters is worked out. It is not Liouville-integrable, however, its two reduced systems are Liouville-integrable, whose Hamiltonian structures are derived by making use of the quadratic-form identity and the γ formula (i.e. the computational formula on the constant γ appeared in the trace identity and the quadratic-form identity). 相似文献
20.
Mesoscopic Transport Characteristics of a Normal—Metal—Superconducting—Grain—Superconductor System
下载免费PDF全文
![点击此处可从《中国物理快报》网站下载免费的PDF全文](/ch/ext_images/free.gif)
FENGJin-Fu XIONGShi-Jie 《中国物理快报》2003,20(6):897-900
We investigate transport properties of a normal-metal-superconducting-grain-superconductor system by the use of the equivalent single-particle multi-channel networks, taking into account the multi-level structure, the Coulomb interaction, and the pair potential on the grain. The dependence of the current on the gate voltage show oscillating behaviour with a period related to 2e of the charge on the grain, reflecting the charge transfer in units of Cooper pairs. The conductance can be enhanced when the pairing parameter is near the Coulomb energy e^2/2C, due to the resonance of the Andreev reflection through the grain. The magnitude of the Andreev reflection as a function of the bias voltage exhibits complicated structures, reflecting the multiple levels, the spin orientations, and the interaction energy on the grain. 相似文献