Gravitational quadrupole radiation of angular momentum

We obtain the quadrupole angular momentum radiation of gravity from the recently obtained covariant conservation law of angular momentum. Our result agrees with that derived from the Landau-Lifshitz energy-momentum pseudotensor.     

The difference between Schrödinger equation derived from Schrödinger map and Landau-Lifshitz equation

We provide an explicit blow up solution of Schrödinger equation derived from Schrödinger map. Consequently we show the non-equivalence between the Schrödinger equation and Landau-Lifshitz equation. We also find that two class of equivariant solutions of Landau-Lifshitz equation are static.     

Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.     

Integration of the Landau-Lifshitz equation with preferred-axis anisotropy by the method of the inverse scattering problem

For the Landau-Lifshitz equation describing the nonlinear dynamics of a ferromagnet with preferred-axis type anisotropy, a closed structure of the Marchenko modification of the inverse scaterring problem method is constructed. The method proposed allows us to obtain and to investigate solutions of the soliton-bion as well as the “weakly bounded” soliton-antisoliton type.     

Gödel-type spacetimes in f(R)-gravity

We focus on one of the famous problems in theoretical physics today: the problem of energy-momentum localization. Although many authors have endeavoured to solve this problem, it has remained unsolved until now. In this work, we consider the generalized version of the Landau-Lifshitz definition in f(R)-Gravity to discuss the energy-momentum localization problem in Gödel-type metrics. We also take into account five popular f(R) models to obtain specific results.     

Microscopic spin-wave theory for yttrium-iron garnet films

Motivated by recent experiments on thin films of the ferromagnetic insulator yttrium-iron garnet (YIG), we have developed an efficient microscopic approach to calculate the spin-wave spectra of these systems. We model the experimentally relevant magnon band of YIG using an effective quantum Heisenberg model on a cubic lattice with ferromagnetic nearest neighbour exchange and long-range dipole-dipole interactions. After a bosonization of the spin degrees of freedom via a Holstein-Primakoff transformation and a truncation at quadratic order in the bosons, we obtain the spin-wave spectra for experimentally relevant parameters without further approximation by numerical diagonalization, using efficient Ewald summation techniques to carry out the dipolar sums. We compare our numerical results with two different analytic approximations and with predictions based on the phenomenological Landau-Lifshitz equation.     

Bergmann-Thomson Energy of a Charged Rotating Black Hole

We obtain the energy distribution associated with a charged rotating (Kerr-Newman) black hole in Bergmann-Thomson formulation. We find that the energy-momentum definitions prescribed by Einstein, Landau-Lifshitz, Papapetrou, Weinberg, and Bergmann-Thomson give the same and acceptable result and also support the Cooperstock hypothesis for energy localization in general relativity. The repulsive effect due to the electric charge and rotation parameters of the metric is also reflected from the energy distribution expression.     

On the energy-momentum in closed universes

Using the Moller, Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum definitions both in general relativity and teleparallel gravity, we find the energy-momentum of the closed universe based on the generalized Bianchi-I type metric.     

Coarse-graining scale and effectiveness of hydrodynamic modeling

We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics from the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., the Landau-Lifshitz one. It is argued that the frame on which the flow of the relativistic hydrodynamic equation is defined must be the energy frame, if the dynamics should be consistent with the underlying RBE. A sketch is also given for derivation of the second-order hydrodynamic equation, i.e., extended thermodynamics, which is accomplished by extending the invariant manifold so that it is spanned by excited modes as well as the zero modes (hydrodynamic modes) of the linearized collision operator. On the basis of thus constructed resummed distribution function, we propose a novel ansatz for the functional form to be used in Grad moment method; it is shown that our theory gives the same expressions for the transport coefficients as those given in the Chapman-Enskog theory as well as the novel expressions for the relaxation times and lengths allowing natural interpretation.     

变系数KP方程新的类孤波解和解析解

用普通Sine-Gordon的行波变换方程，提出了一种新的求解变系数Kaolomtsev-Petviashvili(KP)方程的方法，获得了变系数KP方程新的类孤波解、类Jacobi椭圆函数解和三角函数解. 关键词： 变系数KP方程 Sine-Gordon方程 类椭圆函数解 类孤波解     

Landau-Lifshitz fluctuations in heterotic superstring evaporation

By means of the Landau-Lifshitz theory for nonequilibrium thermodynamical fluctuations we calculate the correlations in the rate of dissipative fluxes of a gas of heterotic superstrings. We briefly comment on the cosmological consequences.     

New explicit exact solutions to a nonlinear dispersive－dissipative equation

Using the first-integral method, we obtain a series of new explicit exact solutions such as exponential function solutions, triangular function solutions, singular solitary wave solution and kink solitary wave solution of a nonlinear dispersive－dissipative equation, which describes weak nonlinear ion-acoustic waves in plasma consisting of cold ions and warm electrons.     

变系数广义KdV方程新的类孤波解和精确解

用普通KdV方程作变换，构造变系数广义KdV方程的解，获得了变系数广义KdV方程新的Jacobi椭圆函数精确解、类孤波解、三角函数解和Weierstrass椭圆函数解. 关键词： KdV方程 变系数广义KdV方程 类孤波解 精确解     

Fluctuating hydrodynamics for a rarefied gas based on extended thermodynamics

We develop a theory of fluctuating hydrodynamics based on extended thermodynamics through studying the 13-variable theory for a monatomic rarefied gas as a representative case. After analyzing the relationship between the present theory and the Landau-Lifshitz theory, we discuss the hierarchy structure of the hydrodynamic fluctuations.     

An Improved F-Expansion Method and Its Application to Coupled Drinfel'd-Sokolov-Wilson Equation

With the aid of computerized symbolic computation, an improved F-expansion method is presented to uniformly construct more new exact doubly periodic solutions in terms of rational formal Jacobi elliptic function of nonlinear partial differential equations (NPDEs). The coupled Drinfel'd-Sokolov-Wilson equation is chosen to illustrate the method. As a result, we can successfully obtain abundant new doubly periodic solutions without calculating various Jacobi elliptic functions. In the limit cases, the rational solitary wave solutions and trigonometric function solutions are obtained as well.     

Dynamics of helimagnets with spin polarised currents

We study analytically, spin polarised current induced dynamics of Dzyaloshinskii-Moriya helimagnets within the phenomenological Landau-Lifshitz framework. Similarities and differences between two popular models of dissipative structures (Gilbert and Landau-Lifshitz dissipation) are explored. Analytical results are obtained and discussed for the magnetisation, the wave number and the velocity of the helical magnetisation structures which are analogous to the behaviour of domain walls under spin polarised current in ferromagnets.