共查询到20条相似文献,搜索用时 15 毫秒
1.
Hajime Nagoya 《Letters in Mathematical Physics》2012,102(3):297-321
We realize affine Weyl group symmetries on the Schr?dinger equations for the quantum Painlevé equations, by fractional calculus. This realization enables us to construct an infinite number of hypergeometric solutions to the Schr?dinger equations for the quantum Painlevé equations. In other words, since the Schr?dinger equations for the quantum Painlevé equations are equivalent to the Knizhnik?CZamolodchikov equations, we give one method of constructing hypergeometric solutions to the Knizhnik?CZamolodchikov equations. 相似文献
2.
Kozo Kobayashi 《Fortschritte der Physik》1989,37(8):599-610
We notice that in the embedding of submanifolds, the fundamental equations are only the Gauss equations for the tangent vectors while the Weingarten equations for the normal equations can essentially be determined by them, and furthermore that the integrability condition of the Weingarten equations, the Ricci equations, are consitently satisfied under that of the Gauss equations. Therefore, the Weingarten and the Ricci equations do not describe essentially independent conditions for embedding. We demonstrate these facts by explicitly constructing the normal vectors from the tangent vectors. 相似文献
3.
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
4.
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
5.
《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
6.
7.
A. A. Zabolotskii 《Journal of Experimental and Theoretical Physics》2011,112(4):642-648
The possibility of forming stable bound plasmon-polariton states in an extended metallic cylinder surrounded by a two-level
medium has been investigated. The dynamics of plasmons is described in the hydrodynamic approximation. It has been shown that
the equations of motion of charge-density bunches and the Bloch equations for the two-level medium are reduced in certain
approximations to integrable equations for both transverse and longitudinal plasmons. In the former case, the initial system
of equations after the application of the slow-envelope approximation is reduced to equations equivalent to the Maxwell-Bloch
equations. In the latter case, the equations describe wave dynamics beyond the slow-envelope approximation. In the approximation
of unidirectional wave propagation, the initial system of equations is reduced to equations related to the reduced Maxwell-Bloch
equations. Soliton and breather-like solutions of the derived equations describe plasmon-exciton self-induced transparency. 相似文献
8.
W. Becker 《Zeitschrift für Physik B Condensed Matter》1981,43(1):87-94
An approximation method is proposed to obtain time dependent solutions of discrete master equations and Fokker-Planck equations. We restrict ourselves to one-dimensional one-step master equations and to one-dimensional F-P equations. Approximate evolution equations for certain statistical averages, e.g. for statistical moments, are formulated and applied for two examples of nonequilibrium phase transitions. 相似文献
9.
We propose a simple and direct method for generating travelling wave solutions for nonlinear integrable equations. We illustrate how nontrivial solutions for the KdV, the mKdV and the Boussinesq equations can be obtained from simple solutions of linear equations. We describe how using this method, a soliton solution of the KdV equation can yield soliton solutions for the mKdV as well as the Boussinesq equations. Similarly, starting with cnoidal solutions of the KdV equation, we can obtain the corresponding solutions for the mKdV as well as the Boussinesq equations. Simple solutions of linear equations can also lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve some new families of KdV equations and show how soliton solutions are also obtained for the higher order equations of the KdV hierarchy using this method. 相似文献
10.
11.
The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations show that lump-like initial conditions evolve into lump soliton solutions for both the Zakharov-Kuznetsov equation and the surface electromigration equations. Solutions of the approximate equations, within their range of applicability, are found to be in good agreement with full numerical solutions of the governing equations. The asymptotic and numerical results predict that localized disturbances will always evolve into nanosolitons. Finally, it is found that dispersive radiation plays a more dominant role in the evolution of lumps for the electromigration equations than for the Zakharov-Kuznetsov equation. 相似文献
12.
Integral equations for particle distribution functions are obtained from Bogolyubov's integrodifferential equations. Bogolyubov's integral equations can be obtained from this set of equations. The equations can also be used to obtain new relations between particle distribution functions. 相似文献
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14.
《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
15.
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
16.
《Journal of Nonlinear Mathematical Physics》2013,20(4):613-640
Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the examples the equivalence problem for the Painleve II equation, Painleve III equation with three zero parameters, Emden equations and for some other equations is solved. 相似文献
17.
Given a choice of a timelike vector field, a particle distribution function in a general curved space-time can be analysed into spherical harmonics; the Liouville and Boltzmann equations can then be written as a set of equations relating these spherical harmonic components. We obtain these equations and the resulting equations for the spherical harmonic moments of the distribution function. An orthonormal tetrad formalism is used as an aid in our calculations; the set of moment equations used can be completed by giving Einstein's field equations as equations for the rotation coefficients of this tetrad. We discuss time and space reversal symmetry properties of the Boltzmann equation, but leave applications of the set of equations obtained to further papers. 相似文献
18.
《Physics letters. A》1988,127(2):99-101
Simplified equations for the nonlinear interaction between whistlers and magnetosonic waves are formulated. These equations describe all the different branches for modulational instabilities of whistler waves, and lead to dispersion relations which are the same as those found from the full set of equations. Our new equations are much more convenient than previously used equations in describing nonlinear whistler wave phenomena. 相似文献
19.
The equivalence between the Bargmann--Wigner (B-W) equations and the
Klein--Gordon (K-G) equations for integral spin, and the Rarita--Schwinger (R-S) equations for half integral spin is established by explicit derivation, starting from the lowest spin cases. It is demonstrated that all the constraints or subsidiary conditions imposed on the K-G or R-S equations are included in the B-W equations. 相似文献
20.
With the help of the continuous symmetries of the Euler equations and the Navier-Stokes equations, respectively, we derive similarity solutions of these equations for two space dimensions. We show that all group theoretical reductions lead to linear nonautonomous or linear autonomous ordinary differential equations for incompressible fluids. 相似文献