共查询到20条相似文献,搜索用时 15 毫秒
1.
LI Ji-Na ZHANG Shun-Li ZUO Su-Li 《理论物理通讯》2008,49(3):545-548
We develop the generalized conditional symmetry (GCS) approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations. We characterize these equations that admit certain higherorder GCSs and show the main reduction procedure by some examples. The obtained reductions cannot be derived within the framework of the standard Lie approach. 相似文献
2.
Lina Ji 《Physica A》2012
This paper considers conditional Lie–Bäcklund symmetries of the radially symmetric nonlinear diffusion equations with source. We obtain a complete list of canonical forms for such equations which admit higher-order conditional symmetries. As a consequence, the solutions of the resulting equations are constructed on the invariant subspaces admitted by the corresponding equations. 相似文献
3.
Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditional symmetries (GCSs) is implemented. The reducibility of the initial-value problem for an evolution equation to a Cauchy problem for a system ofordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry. Complete classification theorems are obtained and some examples are taken to show the main reduction procedure. 相似文献
4.
The functionally generalized variable separation solutions of a general KdV-type equations ut=uxxx + A(u, ux)uxx + B(u, ux) are investigated by developing the conditional Lie-Bäcklund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-Bäcklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations. 相似文献
5.
MA Zheng-Yi 《理论物理通讯》2007,48(2):199-204
We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the (2+1)-dimensional modified Broer- Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations. 相似文献
6.
MA Zheng-Yi 《理论物理通讯》2007,48(8):199-204
We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations. As concrete examples of its application, we apply this method to the (2 1)-dimensional modified Broer-Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations. 相似文献
7.
We analyze (1 + 1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we show how to systematically extend this kinetic theory to obtain higher-order, kinetic equations and to include coupled networks of both excitatory and inhibitory neurons. 相似文献
8.
This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries (GCSs). Complete group classification results are presented, and some examples are given to show the main reduction procedure. 相似文献
9.
ZHANG Shun-Li WANG Yong LOU Sen-Yue 《理论物理通讯》2007,47(6):975-980
The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples. 相似文献
10.
Blair S 《Chaos (Woodbury, N.Y.)》2000,10(3):570-583
Scalar and vector nonlinear nonparaxial evolution equations are developed for propagation in two-dimensions. Using standard soliton scalings, it is found that nonparaxial propagation is accompanied by higher-order linear and nonlinear terms and an effective quintic nonlinear index. The presence of an intrinsic quintic nonlinearity arising from chi((5)) must also be considered at the order of the analysis. These terms represent corrections to the well-known nonlinear Schrodinger equation. Exact and approximate solutions to these higher-order evolution equations are obtained and are shown to exhibit quasi-soliton behavior based on propagation and collision studies. (c) 2000 American Institute of Physics. 相似文献
11.
Initial-value Problems for Extended KdV-Burgers Equations via Generalized Conditional Symmetries 总被引:1,自引:0,他引:1 下载免费PDF全文
We classify initial-value problems for extended KdV-Burgers equations via generalized conditional symmetries. These equations can be reduced to Cauchy problems for some systems of first-order ordinary differential equations. The obtained reductions cannot be derived within the framework of the standard Lie approach. 相似文献
12.
This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as ‘general-dyne’) quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering. 相似文献
13.
Phani Motamarri Mrinal Iyer Jaroslaw Knap Vikram Gavini 《Journal of computational physics》2012,231(20):6596-6621
In the present work, we study various numerical aspects of higher-order finite-element discretizations of the non-linear saddle-point formulation of orbital-free density-functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electron-density is a robust solution procedure for higher-order finite-element discretizations. We next study the convergence properties of higher-order finite-element discretizations of orbital-free density functional theory by considering benchmark problems that include calculations involving both pseudopotential as well as Coulomb singular potential fields. Our numerical studies suggest close to optimal rates of convergence on all benchmark problems for various orders of finite-element approximations considered in the present study. We finally investigate the computational efficiency afforded by various higher-order finite-element discretizations, which constitutes the main aspect of the present work, by measuring the CPU time for the solution of discrete equations on benchmark problems that include large Aluminum clusters. In these studies, we use mesh coarse-graining rates that are derived from error estimates and an a priori knowledge of the asymptotic solution of the far-field electronic fields. Our studies reveal a significant 100–1000 fold computational savings afforded by the use of higher-order finite-element discretization, alongside providing the desired chemical accuracy. We consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite-element basis. 相似文献
14.
15.
We investigate higher-order geometric k-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a
series of images, e.g., in longitudinal studies of Computational Anatomy. Our approach formulates Euler-Poincaré theory in
higher-order tangent spaces on Lie groups. In particular, we develop the Euler-Poincaré formalism for higher-order variational
problems that are invariant under Lie group transformations. The theory is then applied to higher-order template matching
and the corresponding curves on the Lie group of transformations are shown to satisfy higher-order Euler-Poincaré equations.
The example of SO(3) for template matching on the sphere is presented explicitly. Various cotangent bundle momentum maps emerge naturally that
help organize the formulas. We also present Hamiltonian and Hamilton-Ostrogradsky Lie-Poisson formulations of the higher-order
Euler-Poincaré theory for applications on the Hamiltonian side. 相似文献
16.
LIU Cheng-Shi 《理论物理通讯》2006,45(2):219-223
A trial equation method to nonlinear evolution equation
with rank inhomogeneous is given. As applications, the exact
traveling wave solutions to some higher-order nonlinear equations
such as generalized Boussinesq equation, generalized Pochhammer-Chree
equation, KdV-Burgers equation, and KS equation and so on, are
obtained. Among these, some results are new. The proposed method is
based on the idea of reduction of the order of ODE. Some mathematical
details of the proposed method are discussed. 相似文献
17.
从质点系的牛顿动力学方程出发,引入系统的高阶速度能量,导出完整力学系统的高阶Lagrange方程、高阶Nielsen方程以及高阶Appell方程,并证明了完整系统三种形式的高阶运动微分方程是等价的.结果表明,完整系统高阶运动微分方程揭示了系统运动状态的改变与力的各阶变化率之间的联系,这是牛顿动力学方程以及传统分析力学方程不能直接反映的.因此,完整系统高阶运动微分方程是对牛顿动力学方程及传统Lagrange方程、Nielsen方程、Appell方程等二阶运动微分方程的进一步补充.
关键词:
高阶速度能量
高阶Lagrange方程
高阶 Nielsen方程
高阶Appell方程 相似文献
18.
Paul T. Allen Lars Andersson Alvaro Restuccia 《Communications in Mathematical Physics》2011,301(2):383-410
In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian
reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding
to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution
equations is found, which is hyperbolic and has a well-posed initial value problem. We are thus able to solve the initial
value problem for the Hamiltonian evolution equations by means of this equivalent system. We furthermore obtain a blowup criterion
for the membrane evolution equations, and show, making use of the constraint, that one may achieve improved regularity estimates. 相似文献
19.
Conditional Symmetry Groups of Nonlinear Diffusion Equations with x-Dependent Convection and Absorption 总被引:1,自引:0,他引:1
The generalized
conditional symmetry and sign-invariant approaches are developed
to study the nonlinear diffusion equations with x-dependent
convection and source terms. We obtain conditions under which the
equations admit the second-order generalized conditional
symmetries and the first-order sign-invariants on the solutions.
Several types of different generalized conditional symmetries and
first-order sign-invariants for the equations with diffusion of
power law are obtained. Exact
solutions to the resulting equations are constructed. 相似文献
20.
Alexandre M. Tartakovsky Alexander Panchenko Kim F. Ferris 《Journal of computational physics》2011,230(23):8554-8572
We develop a new dimension reduction method for large size systems of ordinary differential equations (ODEs) obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow. The method is also applicable to other large-size classical particle systems with negligibly small variations of particle concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computational advantages of the proposed reduction method, we use it to solve a system of smoothed particle hydrodynamic ODEs describing single-phase and two-phase layered Poiseuille flows driven by uniform and periodic (in space) body forces. For the single-phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution. For the single-phase flow driven by the periodic body force and for the two-phase flows, the higher-order (the first- and second-order) deconvolutions were necessary to obtain a sufficiently accurate solution. 相似文献