共查询到20条相似文献,搜索用时 359 毫秒
1.
《理论物理通讯》2016,(12)
Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. 相似文献
2.
Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. 相似文献
3.
《Fortschritte der Physik》2017,65(12)
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. 相似文献
4.
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
5.
Based on the three-order Lagrangian equations, Hamilton's function of acceleration $H^\ast$ and generalized acceleration momentum P_\alpha ^\ast are defined, and
pseudo-Hamilton canonical equations corresponding to three-order Lagrangian
equations are obtained. The equations are similar to Hamilton's canonical equations
of analytical mechanics in form. 相似文献
6.
7.
In this study, the octonion algebra and its general properties are defined by the Cayley–Dickson’s multiplication rules for
octonion units. The field equations, potential equations and Maxwell equations for electromagnetism are investigated with
the octonionic equations and these equations can be compared with their vectorial representations. The potential and wave
equations for fields with sources are also provided. By using Maxwell equations, a Lorenz-like condition is newly suggested
for electromagnetism. The existing equations including the photon mass provide the most acknowledged Lorenz condition for
the magnetic monopole and the source. 相似文献
8.
Recently, fractional calculus has attracted much attention since it plays an important role in many fields of science and
engineering. Especially, the study on stability of fractional differential equations appears to be very important. In this
paper, a brief overview on the recent stability results of fractional differential equations and the analytical methods used
are provided. These equations include linear fractional differential equations, nonlinear fractional differential equations,
fractional differential equations with time-delay. Some conclusions for stability are similar to that of classical integer-order
differential equations. However, not all of the stability conditions are parallel to the corresponding classical integer-order
differential equations because of non-locality and weak singularities of fractional calculus. Some results and remarks are
also included. 相似文献
9.
《Journal of Nonlinear Mathematical Physics》2013,20(4):458-476
N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are studied by using a generalized version of the dressing method. We first extend the dressing method to the versions with (N + 1) × (N + 1) operators and (2N + 1) × (2N + 1) operators. Then, we obtain three types of N-coupled variable-coefficient equations (N-coupled NLS equations, N-coupled Hirota equations and N-coupled high-order NLS equations). Then, the compatibility conditions are given, which insure that these equations are integrable. Finally, the explicit solutions of the new integrable equations are obtained. 相似文献
10.
The relationship between Einstein's field equations and classical higher spin field equations is investigated using two-component spinor valued differential forms. Linear systems of equations associated to both the vacuum and coupled gravitational matter field equations are constructed. The latter equations are shown to be the integrability conditions of the linear systems. 相似文献
11.
Joshua N. Goldberg 《General Relativity and Gravitation》1974,5(2):183-200
The object of this paper is to relate three equations in the Newman-Penrose system of equations to the conservation laws and, hence, to the equations of motion. To do so, the corresponding result is first obtained using the Einstein equations in a null coordinate system. The Newman-Penrose equations are then analyzed. They are separated into hypersurface, propagation, supplementary, and conservation equations. When all field equations except the three conservation equations have been appropriately satisfied, the desired result follows.Research supported by the National Science Foundation under Grant GP-34641X. 相似文献
12.
13.
K.G. Wang 《Physica A》2008,387(13):3084-3092
Unified model equations hidden in microstructure evolution are discovered in this paper. The governing equations in Lifshitz-Slyozov-Wagner theory, and diffusion screening theory are derived with some approximations from the unified model equations. The governing equations in multiparticle diffusion simulation and phase-field simulation in microstructure evolution are also derived from the unified model equations. The advantages and limitations for different theories and simulations in microstructure evolution are compared in detail. This comparison can guide scientists to select computational tools for their needs in microstructure evolution. The unified model equations can be applied in many new technological fields, such as self-assembly in nanoscience. 相似文献
14.
就一般非完整约束系统,从约束方程满足的变分恒等式出发,利用增广位形流形上的向量场定义三类非自由变分,即非完整变分:vakonomic变分、Hlder变分、Suslov变分,并讨论它们之间的关系以及它们成为自由变分的充要条件.利用非完整变分以及相应的积分变分原理建立两类动力学方程:vakonomic方程和Routh方程或Chaplygin方程.通过vakonomic方程分别与Routh方程和Chaplygin方程比较,得到它们具有共同解的两类充分必要条件.这些条件并不是约束的可积性条件.
关键词:
非完整约束
非完整变分
Chetaev条件
vakonomic动力学 相似文献
15.
It is shown that the equations of motion for a charged massive particle are consequences of the field equations in Kaluza unification theory of gravitation and electromagnetism, i.e., the equations of motion for the particle can be deduced from Kaluza field equations, just as that in Einstein's theory of motion of general relativity the equations of motion for a massive particle are consequences of the Einstein equations. Furthermore, the Lorentz equations for a particle maving in the Maxwell electromagnetic field on the Minkowskian space-time can also be obtained from the Maxwell equations by means of the Kaluze mechanism of the Maxwell theory. 相似文献
16.
17.
A. I. Fomin 《Russian Journal of Mathematical Physics》2012,19(2):159-181
Linear differential operators with complex-valued infinitely differentiable coefficients, linear homogeneous systems of differential equations, and modules over algebras of scalar linear differential operators are considered. Linear differential changes of variables and homomorphisms of special quotient modules (differential homomorphisms) generated by these changes are studied. In terms of differential homomorphisms, relationships between Maxwell equations and equations of electromagnetic potential and between Dirac equations and the Klein-Gordon system of independent equations are described. It is proved that all ordinary nondegenerate linear homogeneous differential equations of some common order and the homogeneous normal systems of the same common order are differentially isomorphic. 相似文献
18.
Frobenius integrable decompositions are introduced for partial differential equations. A procedure is provided for determining a class of partial differential equations of polynomial type, which possess specified Frobenius integrable decompositions. Two concrete examples with logarithmic derivative Bäcklund transformations are given, and the presented partial differential equations are transformed into Frobenius integrable ordinary differential equations with cubic nonlinearity. The resulting solutions are illustrated to describe the solution phenomena shared with the KdV and potential KdV equations. 相似文献
19.
Susanto Chakraborty Pranab Krishna Chanda Dipankar Ray 《International Journal of Theoretical Physics》1995,34(11):2223-2244
Under some assumptions and transformations of variables, Yang's equations forR-gauge fields on Euclidean space lead to conformally invariant equations permitting one to obtain infinitely many other solutions from any solution of these conformally invariant equations. These conformally invariant equations closely resemble the mathematically interesting generalized Lund-Regge equations. Some exact solutions of these conformally in variant equations are obtained. Except for some singular situations, these solutions are self-dual. 相似文献
20.
Cellular automaton fluids 1: Basic theory 总被引:7,自引:0,他引:7
Stephen Wolfram 《Journal of statistical physics》1986,45(3-4):471-526
Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices. Viscosities and other transport coefficients are calculated using the Boltzmann transport equation approximation. Some corrections to the equations of motion for cellular automaton fluids beyond the Navier-Stokes order are given. 相似文献