相关论文: Non-Abelian Kubo Formula and the Multiple Time-Sca…

On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature…

Rossby wave turbulence, as modelled by the Charney-Hasegawa-Mima (CHM) equation, is nonlocal in scale. As a result, the formal stationary Kolmogorov-Zakharov solutions of the Rossby wave kinetic equation, which describe local cascades, are…

Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.

We determine the Lyapunov spectrum of ball quotients arising from cyclic coverings. The computations are performed by rewriting the sum of Lyapunov exponents as ratios of intersection numbers and by the analysis of the period map near…

Exact formulas for the Hall coefficient, modified Nernst coefficient, and thermal Hall coefficient of metals are derived from the Kubo formula. These coefficients depend exclusively on equilibrium (time independent) susceptibilities, which…

In the hydrodynamic theory, the non-equilibrium dynamics of a many-body system is approximated, at large scales of space and time, by irreversible relaxation to local entropy maximisation. This results in a convective equation corrected by…

Efficient numerical methods are still lacking to probe the unconventional dynamics of quantum many-body systems under non-unitary evolution. In this work, we use Faber polynomials to numerically simulate both the dynamics of non-Hermitian…

Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation…

The relativistic kinetic equations describing time evolution and space dependence of the density matrices of polarized photons and electrons interacting via Compton scattering are deduced from the quantum Liouville equation. The induced…

When a quantum system couples strongly to multiple baths then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath. However, capturing such multi-bath system…

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…

We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…

In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of…

In this letter, we study the Alice-Bob peakon system generated from an integrable peakon system through using the strategy of the so-called Alice-Bob non-local KdV approach [13]. Non-local integrable peakon equations are obtained and shown…

A new method for generating analytical expression of quantum Hamiltonian from non-linear differential equation with stationary energy level has been formulated.Further calculation of energy levels have been carried out analytically using…

A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The…

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized…

Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and…

This paper deals with the following Petrovsky equation with damping and nonlinear source \[u_{tt}+\Delta^2 u-M(\|\nabla u\|_2^2)\Delta u-\Delta u_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-boundary value conditions, where $M(s)=a+…

The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and…