量子Yang-Baxter方程的1/2旋子的奇异上三角型解(Ⅱ)(英文)

In these two papers (Ⅰ) and (Ⅱ),the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given.In the Paper (Ⅱ),we give the general solutions of the Yang-Baxter equation in this case.     

m-KdV-Sine-Gordon方程和m-KdV-Sinh-Gordon方程的行波解(英文)

By using the function transformation and proper Sub-ODE, exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained, from which exact travelling wave solutions of the m-KdV equation, the Sine-Gordon equation and the Sinh-Gordon equation are derived.     

The Singular Upper Triangle Type Solutions with Spin 1/2 of Quantum Yang-Baxter Equation （I）

In these two papers （I） and （II）, the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper （I）, we give the Yang-Baxter equation and give the general solutions of some function equations for the next paper.     

Energy-Preserving $H^1$--Galerkin Schemes for the Hunter-Saxton Equation

We consider the numerical integration of the Hunter–Saxton equation, which models the propagation of weakly nonlinear orientation waves. For the equation, we present two weak forms and their Galerkin discretizations. The Galerkin schemes preserve the Hamiltonian of the equation and can be implemented with cheap H~1 elements. Numerical experiments confirm the effectiveness of the schemes.     

Compressible Limit of the Nonlinear Schrdinger Equation with Different-Degree Small Parameter Nonlinearities

The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singularities in the limit system.On the one hand,the existence and uniqueness of the classical solution are proved for the dispersive perturbation of the quasi-linear symmetric system corresponding to the initial value problem of the above nonlinear Schrdinger equation.On the other hand,in the limi...     

A multiscale Galerkin method for the hypersingular integral equation reduced by the harmonic equation

The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersingular integral equation with the map x=cot(θ/2). Second, we initiate the study of the multiscale Galerkin method for the 2π-periodic hypersingular integral equation. The trigonometric wavelets are used as trial functions. Consequently, the 2j+1 × 2j+1 stiffness matrix Kj can be partitioned j×j block matrices. Furthermore, these block matrices are zeros except main diagonal block matrices. These main diagonal block matrices are symmetrical and circulant matrices, and hence the solution of the associated linear algebraic system can be solved with the fast Fourier transform and the inverse fast Fourier transform instead of the inverse matrix. Finally, we provide several numerical examples to demonstrate our method has good accuracy even though the exact solutions are multi-peak and almost singular.     

Ulam-Hyers Stability of Trigonometric Functional Equation with Involution

The present work aims to determine the solution of trigonometric functional equation f with involution from group to field by using the properties of involution function,and the solution and Ulam-Hyers stability of the trigonometric functional equation are also discussed.Furthermore,this method generalizes the main theorem and gives the supplement in some reference.     

CONDITIONS FOR OSCILLATION OF NEUTRAL DELAY DIFFERENTIAL EQUATIONS

In this paper,we study one type of odd-order neutral delay differential equation. Suffcient conditions for the oscillation of every solution to this type of differential equation are given.     

All Commuting Solutions of a Quadratic Matrix Equation for General Matrices

Using the Jordan canonical form and the theory of Sylvester’s equation, we ?nd all the commuting solutions of the quadratic matrix equation AXA = XAX for an arbitrary given matrix A.     

PERIODIC SOLUTIONS TO A KIND OF NEUTRAL DIFFERENTIAL SYSTEM:VIA (h,k)-DICHOTOMY

In this paper, based on the theory of (h, k)-Dichotomy of linear system and Kras-noselskii’s fixed point theorem, we study the existence of periodic solutions to a neutral differential equation. Some new sufficient conditions are obtained to guarantee the existence and uniqueness of T-periodic solution to the equation.     

ON THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, we consider a higher order differential equation and obtain a precise estimate of the order of growth and the hyper-order of solutions to the equation.     

POSITIVE WEIGHTED PSEUDO-ALMOST PERIODIC SOLUTIONS TO INFINITE DELAY INTEGRAL EQUATION

This paper studies the existence of almost periodic type solutions to the nonlinear infinite delay integral equation. By means of the fixed theorem on a suitable space with Hilbert’s projective metric, we establish some sufficient conditions for the existence of positive weighted pseudo-almost periodic solutions to the equation.     

ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.     

LIMIT CYCLES FOR A CLASS OF FIFTH-ORDER DIFFERENTIAL EQUATIONS

In this paper, we study a fifth-order differential equation. Using the averaging theory, we investigate the limit cycles of the equation.     

ALMOST PERIODICITY FOR AN IMPULSIVE PURE DELAY LOGISTIC EQUATION

By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic solutions to the equation are obtained.     

OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.     

The multi-soliton solutions of the CH-γ equation

This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation method.Some properties of the soliton solutions are different from the CH equation.     

A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line

In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, onecusp soliton solution is expressed in terms of the Riemann-Hilbert problem.     

Hodge integrals with one λ-class

Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space.ELSV formula connects the Hodge integrals with Hurwitz numbers,and the generating function of Hurwitz numbers satisfies the cut-and-join equation.Therefore,it is natural to consider how to use the cut-and-join equation for Hurwitz numbers to compute Hodge integrals which appear in ELSV formula.In this paper,at first,we will review the method introduced in Goulden et al.’s paper to get the λ g conjecture for Hodge integral.Through some variables transformation,the generating function of Hurwitz number becomes a symmetric polynomial which satisfies a symmetrized cut-and-join equation.By comparing the coefficients of the lowest degree term of both sides in this equation,we can get the λ g conjecture.Then,in a similar way,we obtain our main result in this paper:a recursive formula for Hodge integral of type contains only one λ g 1-class.We also point out that our results are closely related to the degree 0 Virasoro conjecture for a curve.     

STABILITY OF DISSIPATIVE BOLTZMANN EQUATION FOR ONE-DIMENSIONAL GRANULAR GASES

In this paper, the stability of the dissipative Boltzmann equation is investigated under the influence of an external source of energy for the spatially homogeneous case. Using probability distance, we give an estimate to show the uniform stability of the solution.