共查询到20条相似文献,搜索用时 46 毫秒
1.
REN Wen-Xiu Alatancang 《理论物理通讯》2007,48(2):211-214
In the present paper, we identify the integrability of the third-order nonlinear evolution equation ut = (1/2)((uxz + u)^-2)z in a Hamiltonian viewpoint. We prove that the recursion operator obtained by S.Yu. Sakovich is hereditary, and then deduce a bi-Hamiltonian structure of the equation by using some decomposition of the hereditary operator. A hierarchy associated to the equation is also shown. 相似文献
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Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that thehierarchy possesses a Hamiltonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way. 相似文献
3.
LOU Senyue 《理论物理通讯》1997,28(1):41-50
Starting from any one of hereditary symmetries, we can construct a type of integrable models with arbitrary dimensions. The models with different dimensions obtained from a same hereditary symmetry possess a common recursion operator. The symmetry structures of the models are studied in their potential forms. Using the formal series symmetry approach, we can get various sets of formal series symmetries with some arbitrary functions. Generally, these sets of series symmetries are not truncated for arbitrary functions. The series symmetries wiU all be truncated if the arbitrary functions are fixed as polynomials. Some sets of nontruncated symmetries constitute generalized Virasoro algebras. The more details about the symmetries and algebras are discussed for a concrete (3+1)-dimensional KdV equation. 相似文献
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Mahouton Norbert Hounkonnou Partha Guha Tudor Ratiu 《Journal of Nonlinear Mathematical Physics》2016,23(1):47-73
Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 –245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quasi-associative. Its link to geometry and nonlinear systems of hydrodynamic type is also recalled. Further, the criteria of skew-symmetry, derivation and Jacobi identity making this algebra into a Lie algebra are derived. The coboundary operators are defined and discussed. We deduce the hereditary operator and its generalization to the corresponding 3–ary bracket. Further, we derive the so-called ρ–compatibility equation and perform a phase-space extension. Finally, concrete relevant particular cases are investigated. 相似文献
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Variational principles yielding upper and lower bounds on transport coefficients can readily be applied to the Boltzmann equation, provided it has the form of a linear, inhomogeneous integrodifferential equation with a Hermitian operator acting on the deviation from equilibrium of the distribution function. In transport problems involving a magnetic field or an alternating electric field, this operator is non-Hermitian. By suitably transforming the transport equation, we show how Variational principles may still give upper and lower bounds. The bounds are used for considering the frequency-dependent conductivity associated with a general scattering operator, and the longitudinal magnetoresistivity in the relaxation time approximation for the scattering operator. Explicit results are presented for (1) the frequency-dependent conductivity of a charged Fermi liquid and (2) the longitudinal magnetoresistivity for a weakly anisotropic Fermi surface. 相似文献
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XUXi-Xiang YANGHong-Xiang DINGHai-Yong 《理论物理通讯》2005,44(1):1-7
A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constants in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulations a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy. 相似文献
10.
A difference Ha-miltonian operator with three arbitrary constants is presented. When the arbitrary constants -in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulation, a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy. 相似文献
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波动方程深度偏移的局部裂步Fourier传播算子 总被引:2,自引:1,他引:1
针对裂步Fourier传播算子在速度强横向变化介质中的不足,将算子的框架展开方法应用于Fourier传播算子中的相移算子,提出了一种波场传播的局部裂步Fourier传播算子,并把它应用于波动方程叠前深度偏移成像.这个局部裂步Fourier传播算子是由相空间(空间-波数)-频率域的相移算子和空间-频率域的窗口时移算子两部分组成.与波数-频率域的空间全局性相移算子不同,相空间-频率域的相移算子具有很好的空间局部性.通过在国际标准的SEG-EAGE二维盐丘模型的波动方程叠前深度偏移成像数值试验,证明局部Fourier传播算子不仅具有很好的稳定性,而且还特别适用于速度强横向变化介质. 相似文献
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A noise erosion operator based on partial differential equation (PDE) is introduced, which has an excellent ability of noise removal and edge preservation for two-dimensional (2D) gradient data. The operator is applied to estimate a new diffusion coefficient. Experimental results demonstrate that anisotropic diffusion based on this new erosion operator can efficiently reduce noise and sharpen object boundaries. 相似文献
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We present a class of asymptotic-preserving (AP) schemes for the nonhomogeneous Fokker–Planck–Landau (nFPL) equation. Filbet and Jin [16] designed a class of AP schemes for the classical Boltzmann equation, by penalization with the BGK operator, so they become efficient in the fluid dynamic regime. We generalize their idea to the nFPL equation, with a different penalization operator, the Fokker–Planck operator that can be inverted by the conjugate-gradient method. We compare the effects of different penalization operators, and conclude that the Fokker–Planck (FP) operator is a good choice. Such schemes overcome the stiffness of the collision operator in the fluid regime, and can capture the fluid dynamic limit without numerically resolving the small Knudsen number. Numerical experiments demonstrate that the schemes possess the AP property for general initial data, with numerical accuracy uniformly in the Knudsen number. 相似文献
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用Heisenberg-Weyle(简称H-W)群直积SU(2)群上的相干态表述了原 子-辐射场相互作用系统的Heisenberg运动方程。引入一个算符振幅函数,将Heisenberg绘 景中算符运动方程转化成可分离变量的偏微分方程,给出了方程的形式解以及时间演化算符 在该表述下的表示。 相似文献
15.
An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrödinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrödinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones. 相似文献
16.
Abdul-Majid Wazwaz 《Waves in Random and Complex Media》2018,28(3):533-543
A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV–nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions. 相似文献
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FAN Hong-Yi TANG Xu-Bing 《理论物理通讯》2008,49(5):1169-1172
Using the technique of integration within an ordered product (IWOP) of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation that is an operator generalization of the solution of thermo conduction equation. Then we seach for the solution of operator Fredholm integration equations, which provides us with a new approach for deriving some operator identities. 相似文献
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A local meson operator is constructed from the path-ordered operator on QCD2. The meson operator satisfies the Klein-Gordon equation with the mass identical to the eigenvalue of the 't Hooft equation. The interaction of the meson is shown to be nonlocal and to have a coupling proportional to 1/Nc. 相似文献
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Construction of a kinetic equation for a dynamical system interacting with a boson field in the case of spatial inhomogeneity
is based on a method expounded in [1–3]. In the present article, it is shown that approaches considered in [1, 2] can be generalized
for the case of spatial inhomogeneity. An arbitrary operator function that depends on the momentum and spatial variable is
applied for derivation of a kinetic equation. We consider a method of studying an electron-phonon system by means of exclusion
of boson operators from corresponding operator equations. In particular, interaction of an electron with a boson field is
described by a kinetic equation for a polaron in the case of spatial inhomogeneity. In the relevant limit, a Boltzmann equation
for the polaron is obtained. 相似文献
20.
A 3-dimensional Lie algebra sμ(3) is obtained with the help of the known Lie algebra. Based on the sμ(3), a new discrete 3 × 3 matrix spectral problem with three potentials is constructed. In virtue of discrete zero curvature equations, a new matrix Lax representation for the hierarchy of the discrete lattice soliton equations is acquired. It is shown that the hierarchy possesses a Hamiltonian operator and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals. 相似文献