求解mKdV方程呼吸子的一个新方法

给出了一种求mKdV方程呼吸子解的新方法.通过非线性变换把mKdV方程化成一种新的形式,假设其解具有分离变量的形式,在特定的条件下得到了该方程的一个特解——呼吸子解(也称为双子解).

Dynamics of Nonlinear Waves in(2+1)-Dimensional Extended Boiti-Leon-Manna-Pempinelli Equation

Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.

Double-Pole Solution and SolitonAntisoliton Pair Solution of MNLSE/DNLSE Based upon Hirota Method

Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.

Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

Kortweg-de Vries （KdV）-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV （GCCKdV） equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented： （i） two solitons merge and separate from each other periodically; （ii） two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; （iii） two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing.

Application of Computer Algebra in Solving Chaffee-Infante Equation

In this paper, a series of two line-soliton solutions and double periodic solutions of Chaffee-Infante equation have been obtained by using a new transformation. Unlike the existing methods which are used to find multiple soliton solutions of nonlinear partial differential equations, this approach is constructive and pure algebraic. The results found here are tested on computer and therefore their validity is ensured.

Soliton Solutions for a Negative Order AKNS Equation

In this short paper,bilinear form of a negative order AKNS equation is given.The N-soliton solutions areobtained through Hiorta's direct method.

Multiple Periodic-Soliton Solutions for(3+1)-Dimensional Jimbo-Miwa Equation

2N line-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation can be presented by resorting tothe Hirota bilinear method.In this paper,N periodic-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equationare obtained from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs.

Soliton Solutions for a Negative Order AKNS Equation Hierarchy

In this paper,bilinear form of a negative order AKNS equation hierarchy is given.The soliton solutionsare obtained through Hiorta's direct method.

Hooke's Atom in an Arbitrary External Electric Field: Analytical Solutions of Two-Electron Problem by Path Integral Approach

By using the path integral approach, we investigate the problem of Hooke＇s atom （two electrons interacting with Coulomb potential in an external harmonic-oscillator potential） in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.

A New Auto-Backlund Transformation and Two-Soliton Solution for (3+l)-Dimensional Jimbo-Miwa Equation

Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation （BT） for （3-k l）-Dimensional Jimbo-Miwa （JM） equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the （3＋1）-Dimensional JM equation is obtained.

A Generalized Hirota Ansatz to Obtain Soliton-Like Solutions for a (3+l)-Dimensional Nonlinear Evolution Equation

Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.

Solution to Operator Fredholm Equation in Bipartite Entangled State Representation and Its Applications

Based on the bipartite entangled state representation and using the technique of integration within an ordered product （IWOP） of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and new relations about the two-variable Hermite polynomials.

A Simple Approach to Derive a Novel N-Soliton Solution for a (3+1)-Dimensional Nonlinear Evolution Equation

Based on the Hirota bilinear form, a simple approach without employing the standard perturbation technique, is presented for constructing a novel N-soliton solution for a （3＋1）-dimensional nonlinear evolution equation. Moreover, the novel N-soliton solution is shown to have resonant behavior with the aid of Mathematica.

Analytical Modeling of Threshold Voltage for Double-Gate MOSFET Fully Comprising Quantum Mechanical Effects

The analytical solutions to 1D Schrdinger equation (in depth direction) in double gate (DG) MOSFETs are derived to calculate electron density and threshold voltage.The non uniform potential in the channel is concerned with an arbitrary depth so that the analytical solutions agree well with numerical ones.Then,an implicit expression for electron density and a closed form of threshold voltage are presented fully comprising quantum mechanical (QM) effects.This model predicts an increased electron density with an increasing channel depth in subthreshold region or mild inversion region.However,it becomes independent on channel depth in strong inversion region,which is in accordance with numerical analysis.It is also concluded that the QM model,which barely considers a box like potential in the channel,slightly over predicts threshold voltage and underestimates electron density,and the error increases with an increasing channel depth or a decreasing gate oxide thickness.

Mechanism of aluminum corrosion in LiFSI-based electrolyte at elevated temperatures

Lithium bis(fluorosulfonyl)imide(LiFSI) is a promising replacement for lithium hexafluorosphate due to its excellent properties. A solution to the corrosion of aluminum(Al) current collectors by LiFSI at elevated temperatures is essential. The mechanisms of Al corrosion in LiFSI-based electrolyte at 45 ℃ were studied with density functional theory calculations and spectroscopic investigations. It is found that the irregular, loose and unprotected AlF3 materials caused by the dissolution of co-generated Al(FSI)3 can exacerbate Al corrosion with the increase of temperature. Lithium bis(oxalate)borate(LiBOB) can effectively inhibit the Al corrosion with a robust and protective interphase;this can be attributed to the interfacial interactions between the Al foil and electrolyte. Boron-containing compounds promote the change from AlF3 to LiF, which further reinforces interfacial stability. This work allows the design of an interface to Al foil using LiFSI salt in lithium-ion batteries.

Optical Conductivity of Impurity-Doped Parabolic Quantum Wells in an Applied Electric Field

The optical conductivity of impurity-doped parabolic quantum wells in anapplied electric field is investigated with the memory-function approach, and the analyticexpression for the optical conductivity is derived. With characteristic parameters pertaining toGaAs/Ga_(1-x)Al_xAs parabolic quantum wells, the numerical results are presented. It is shown that,the smaller the well width, the larger the peak intensity of the optical conductivity, and the moreasymmetric the shape of the optical conductivity; the optical conductivity is more sensitive to theelectric field, the electric Geld enhances the optical conductivity; when the dimension of thequantum well increases, the optical conductivity increases until it reaches a maximum value, andthen decreases.

Optical Operator Method in Two-Mode Case and Entangled Fresnel Operator's Decomposition

Based on the entangled Fresnel operator （EFO） proposed in [Commun. Theor. Phys. 46 （2006） 559], the optical operator method studied by the IWOP technique （Ma et al., Commun. Theor. Phys. 49 （2008） 1295） is extended to the two-mode case, which gives the decomposition of the entangled Fresnel operator, corresponding to the decomposition of ray transfer matrix [A, B, C, D]. The EFO can unify those optical operators in two-mode case. Various decompositions of EFO into the exponential canonical operators are obtained. The entangled state representation is useful in the research.

Painlevé Analysis,Soliton Solutions and Bcklund Transformation for Extended (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations in Fluid Mechanics via Symbolic Computation

This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plasmas and other fields.Painleve analysis is passed through via symbolic computation.Bilinear-form equations are constructed and soliton solutions are derived.Soliton solutions and interactions are illustrated.Bilinear-form Backlund transformation and a type of solutions are obtained.

Two-grid method for characteristic mixed finite-element solutions of nonlinear convection-diffusion equations

A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.

Soliton Solutions and Bilinear Bcklund Transformation for Generalized Nonlinear Schrdinger Equation with Radial Symmetry

Investigated in this paper is the generalized nonlinear Schrodinger equation with radial symmetry. With the help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method. B^cklund transformation in the bilinear form is presented, through which a new solution is constructed. Graphically, we have found that the solitons are symmetric about x = O, while the soliton pulse width and amplitude will change along with the distance and time during the propagation.