Bäcklund Transformations,Solitary Waves,Conoid Waves and Bessel Waves of the (2+1)-Dimensional Euler equation

Some simple special Bäcklund transformation theorems are proposed and utilized to obtain exact solutions for the (2+1)-dimensional Euler equation. It is found that the (2+1)-dimensional Euler equation possesses abundant soliton or solitary wave structures, conoid periodic wave structures and the quasi-periodic Bessel wave structures on account of the arbitrary functions in its solutions. Moreover, all solutions of the arbitrary two dimensional nonlinear Poisson equation can be used to construct exact solutions of the (2+1)-dimensional Euler equation.     

Dynamic analysis of frames with viscoelastic dampers modelled by rheological models with fractionalderivatives

Frame structures with viscoelastic dampers mounted on them are considered in this paper. Viscoelastic (VE) dampers are modelled using two, three-parameter, fractional rheological models. The structures are treated as elastic linear systems. The equation of motion of the whole system (structure with dampers) is written in terms of state-space variables. The resulting matrix equation of motion is the fractional differential equation. The proposed state space formulation is new and does not require matrices with huge dimensions. The paper is devoted to determine the dynamic properties of the considered structures. The nonlinear eigenvalue problem is formulated from which the dynamic parameters of the system can be determined. The continuation method is used to solve the nonlinear eigenvalue problem. Moreover, results of typical calculations are presented.     

Periodic Structures of Rossby Wave under Influence of Dissipation

A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, we derive the rotational KdV （rKdV for short） equation. And then, with the help of Jaeobi elliptie functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.     

Nonlinear dynamics associated with rotating magnetized electron-positron-ion plasmas

By using the hydrodynamic equations of electrons and positrons and Poisson equation with stationary ions, a three-dimensional extended Zakharov-Kuznetsov (EZK) equation is derived for small but finite amplitude nonlinear Langmuir structures (solitary and shock pulses) The EZK equation is solved analytically and the features of the nonlinear excitations are investigated numerically. Furthermore, the propagation condition for the nonlinear structures is examined.     

On the morphological similarities between networklike structures in viscoelastic polymer systems and the large-scale structure of the universe

Networklike structures are observed in various materials and nature. The networklike structures in viscoelastic phase separation of polymer mixtures have been explained by a model with a couple of hydrodynamic equations. On the other hand, the large-scale structure of the universe has been explained by a multi-dimensional extension of the Burgers equation. The networklike structures of the two very different systems have some morphological similarities. To see origins of the similarities and differences, the Burgers equation is derived from the model of the polymer mixtures using several approximations. The meaning of the approximations is discussed in connection with the morphology.     

Structures of Equatorial Envelope Rossby Wave Under a Generalized External Forcing

The cubic nonlinear Schrodinger (NLS for short) equation with a generalized external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of a new transformation, Jacobi elliptic functions,and elliptic equation. It is shown that different types of resonant phase-locked diabatic heating play different roles in structures of equatorial envelope Rossby wave.     

A Variable Separation Approach to Solve the Integrable and Nonintegrable Models:Coherent Structures of the (2 + 1)-Dimensional KdV Eqnation

We study the localized coherent structures ofa generally nonintegrable (2 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.     

Defect-deformational Kuramoto-Sivashinsky equation and formation of surface nano- and microstructures under the laser and ion-beam irradiation

Systematic numerical investigation of recently derived isotropic 2D defect-deformational (DD) Kuramoto-Sivashinsky (KS) equation that desribes the surface relief of the stressed nanolayer with nonequilibrium mobile point defects is carried out. It is demonstrated that the DDKS equation describes the formation of the surface DD structures of three main types: lamellar-like structures, and disordered and hexagonally ordered ensembles of nanoparticles. The generalization of the DDKS equation to the anisotropic diffusion of surface defects is performed and the numerical solution to the derived anisotropic DDKS equation is obtained to describe the formation of 1D surface DD ripples. The calculated results are compared with the experimental data on the formation of surface nano- and microstructures on solid surface under the laser and ion-beam irradiation.     

Nonlinear Waves in Inhomogeneous Cylindrical Shells: A New Evolution Equation

A fifth-order evolution equation with cubic nonlinearity is derived for describing the wave processes in nonlinearly elastic, inhomogeneous deformed structures. The Backlund transform and an exact soliton-like solution are obtained for this equation. A relation between this equation and the nonlinear Schrödinger equation is pointed out.     

Explicit solutions of two nonlinear dispersive equations with variable coefficients

A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa-Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions.     

Some remarks on coherent structures out of chaos in planetary atmospheres and oceans

In the context of planetary atmospheres and oceans, it is natural to define "coherent structures" as "long-lived," or "solitary," Rossby vortices. These can be described by the generalized Charney-Obukhov equation (in fluid dynamics) or the analogous generalized Hasegawa-Mima equation (in plasma physics). These two equations contain KdV-type nonlinearities which (together with the compensating dispersive spreading) determine the formation of the coherent structures and explain the clear-cut cyclonic/anticyclonic asymmetry observed experimentally in long-lived planetary Rossby vortices. Examples are given of natural vortices which are (and which are not) coherent structures.     

Kinetics of quasiballistic transport in nanoscale semiconductor structures: is the ballistic limit attainable at room temperature?

Electron transport in nanoscale semiconductor structures is theoretically investigated to answer the question of whether or not the ballistic limit is really attainable under room temperature operation. The semiclassical Boltzmann transport equation is solved analytically under the relaxation time approximation for n(+)-n-n(+) test structures. We demonstrate that the solution of the Boltzmann transport equation exhibits a boundary layer structure near the potential barrier and thus the scatterings in the active region cannot be neglected even in nanoscale structures, as far as they are operated at room temperature under high applied voltages.     

Periodic Structure of Equatorial Envelope Rossby Wave Under Influence of Diabatic Heating

A simple shallow-water model with influence of diabatic heating on a β-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schro^edinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacob/elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form.     

A Super Extension of Heisenberg Hierarchy

A super Heisenberg equation associated with a 3 × 3 matrix spectral problem is proposed take advantage of the zero-curvature equation. Its super bi-Hamiltonian structures are obtained through super trace identity and infinitely many conserved quantities of the super Heisenberg equation are constructed by means of spectral parameter expansions.     

RPA equation embedded into infinite-dimensional Fock space F ∞

To clear up both algebraic and geometric structures for integrable systems derived from self-consistent field theory, in particular, geometric aspect of the random-phase-approximation (RPA) equation is exhibited on the basis of the viewpoint of symmetry of the evolution equation. The RPA equation for an infinite-dimensional Grassmannian is constructed.     

Lie Algebraic Structures and Integrability of Long-Short Wave Equation in （2＋1）Dimensions

The hidden symmetry and integrability of the long-short wave equation in (2 1) dimensions are considered using the prolongation approach. The internal algebraic structures and their linear spectra are derived in detail which show that the equation is integrable.     

(2+1)维破裂孤子方程的多方孤子解及其混沌行为

利用投射方程法和变量分离法,得到(2+1)维破裂孤子方程的新显式精确解. 根据得到的孤立波解,利用 Weierstrassp 函数,构造出多方孤子局域结构. 利用两个混沌系统研究了破裂孤子方程的混沌行为. 关键词： 投射方程法 破裂孤子方程 多方孤子 混沌行为     

Fractional dynamics of coupled oscillators with long-range interaction

We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0相似文献   

An inverse algorithm for reconstructing the acoustic parameters of layered medium

I.IntroductionThcinvcrsescattcringprob1cmisbasicinarcassuchasradar,sonar,geophysica1explora-honandnondestructivctesting.Whenthescatteringobjectisaconstitutiveparametersvaryinacontinuousmannerandtheinvcrseproblcmistodctcrmineoneormoreoftheseparametcrsfromtheobserveddata.Muchofthcpreviousworkonthisproblcmforthecaseofp1anewaveatnormalincidencchasconsistcdofderivingaSchr6dingerequationfromthebasicacousticandstrcss-straincquations,andthenreconstruchngthepotentialappearinginthisequationbyusingtheGe…     

mKdV-sine-Gordon方程丰富的相互作用解

基于mKdV-sine-Gordon方程的Wronsk解的形式和结构,提出了Wronsk形式展开法,通过这一方法求得了该方程的丰富的相互作用解,该方法的主要特征是不要求Wronsk行列式元素满足线性偏微分方程组。