A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing....A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.展开更多
In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by usi...In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.展开更多
A theoretical model for mixed lubrication with more accurate contact length has been developed based on the average volume flow model and asperity flattening model,and the lubricant volume flow rate and outlet speed r...A theoretical model for mixed lubrication with more accurate contact length has been developed based on the average volume flow model and asperity flattening model,and the lubricant volume flow rate and outlet speed ratio are determined by integrating differential equations based on rolling parameters.The lubrication characteristics at the roll-strip interface with different surface roughness,rolling speed,reduction and lubricant viscosity are analyzed respectively.Additionally,the average volume flow rates of lubricant under different rolling conditions are calculated and used to explain the change rule of lubrication characteristics.The developed scheme is able to determine the total pressure,lubricant pressure,film thickness and real contact area at any point within the work zone.The prediction and analysis of mixed lubrication characteristics at the interface is meaningful to better control the surface quality and optimize the rolling process.展开更多
In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-...In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.展开更多
In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated meth...In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated method. A group of sufficient conditions are given to guarantee asymptotic stability of zero solutions of systems.展开更多
We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the e...We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.展开更多
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-pol...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.展开更多
This paper concerns with the existence of solutions for the following fractional Kirchhoff problem with critical nonlinearity：where （-△）s is the fractional Laplacian operator with 0 〈 s 〈 1, 2s＊ = 2N/（N - 2s）...This paper concerns with the existence of solutions for the following fractional Kirchhoff problem with critical nonlinearity：where （-△）s is the fractional Laplacian operator with 0 〈 s 〈 1, 2s＊ = 2N/（N - 2s）, N 〉 2s, p ∈ （1,2s＊）, θ∈ [1, 2s＊/2）, h is a nonnegative function and A is a real positive parameter. Using the Ekeland variational principle and the mountain pass theorem, we obtain the existence and multiplicity of solutions for the above problem for suitable parameter A 〉 0. Furthermore, under some appropriate assumptions, our result can be extended to the setting of a class of nonlocal integro-differential equations. The remarkable feature of this paper is the fact that the coefficient of fractional Laplace operator could be zero at zero, which implies that the above Kirchhoff problem is degenerate. Hence our results are new even in the Laplacian case.展开更多
By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability ...A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectie map and a completely integrable tinite-dimensionai Hamiltonian system.展开更多
This paper studies the asymptotic stability of traveling we solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinea...This paper studies the asymptotic stability of traveling we solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some "nice structure" of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.展开更多
In the literature （Tan and Wang, 2010）, Tan and Wang investigated the convergence of the split-step backward Euler （SSBE） method for linear stochastic delay integro-differential equations （SDIDEs） and proved the...In the literature （Tan and Wang, 2010）, Tan and Wang investigated the convergence of the split-step backward Euler （SSBE） method for linear stochastic delay integro-differential equations （SDIDEs） and proved the mean-square stability of SSBE method under some condition. Unfortu- nately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory.展开更多
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for...A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.展开更多
Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of o...Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of overdetermined partial differential equations: Given a system of quasi-linear PDEs of first order for one unknown function we find a necessary and sufficient condition for the existence of solutions in terms of the second jet of the coefficients. This generalizes to certain quasi-linear systems of first order for several unknown functions.展开更多
The electrohydrodynamic stability of a self-gravitating streaming compound jet has been investigated for all modes of perturbation. The jets are immersed in a dielectric motionless tenuous medium pervaded by varying e...The electrohydrodynamic stability of a self-gravitating streaming compound jet has been investigated for all modes of perturbation. The jets are immersed in a dielectric motionless tenuous medium pervaded by varying electric field. A second-order integrodifferential equation of Mathieu type has been derived and some reported works are recovered as limiting cases from it.展开更多
基金supported by National Natural Science Foundation of China under Grant No. 10575087the Natural Science Foundation of Zhejiang Province under Grant No. 102053
文摘A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.
文摘In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.
基金Project(2012BAF09B04)supported by the National Key Technology Research and Development Program of China
文摘A theoretical model for mixed lubrication with more accurate contact length has been developed based on the average volume flow model and asperity flattening model,and the lubricant volume flow rate and outlet speed ratio are determined by integrating differential equations based on rolling parameters.The lubrication characteristics at the roll-strip interface with different surface roughness,rolling speed,reduction and lubricant viscosity are analyzed respectively.Additionally,the average volume flow rates of lubricant under different rolling conditions are calculated and used to explain the change rule of lubrication characteristics.The developed scheme is able to determine the total pressure,lubricant pressure,film thickness and real contact area at any point within the work zone.The prediction and analysis of mixed lubrication characteristics at the interface is meaningful to better control the surface quality and optimize the rolling process.
文摘In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.
文摘In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated method. A group of sufficient conditions are given to guarantee asymptotic stability of zero solutions of systems.
文摘We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.
基金Supported by the National Natural Science Foundation of China (12074295)。
文摘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.
基金supported by National Natural Science Foundation of China(Grant Nos.11601515 and 11401574)the Fundamental Research Funds for the Central Universities(Grant No.3122015L014)the Doctoral Research Foundation of Heilongjiang Institute of Technology(Grant No.2013BJ15)
文摘This paper concerns with the existence of solutions for the following fractional Kirchhoff problem with critical nonlinearity：where （-△）s is the fractional Laplacian operator with 0 〈 s 〈 1, 2s＊ = 2N/（N - 2s）, N 〉 2s, p ∈ （1,2s＊）, θ∈ [1, 2s＊/2）, h is a nonnegative function and A is a real positive parameter. Using the Ekeland variational principle and the mountain pass theorem, we obtain the existence and multiplicity of solutions for the above problem for suitable parameter A 〉 0. Furthermore, under some appropriate assumptions, our result can be extended to the setting of a class of nonlocal integro-differential equations. The remarkable feature of this paper is the fact that the coefficient of fractional Laplace operator could be zero at zero, which implies that the above Kirchhoff problem is degenerate. Hence our results are new even in the Laplacian case.
基金This research is supported by the Tianyuan Mathematics Foundation (No. 10226007) and the Science Foundation of Xinjiang University
文摘By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
基金Supported by the Science and Technology Plan Projects of the Educational Department of Shandong Province of China under GrantNo. J08LI08
文摘A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectie map and a completely integrable tinite-dimensionai Hamiltonian system.
文摘This paper studies the asymptotic stability of traveling we solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some "nice structure" of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.
基金supported by the Fundamental Research Funds for the Central Universities under Grant No. 2012089:31541111213China Postdoctoral Science Foundation Funded Project under Grant No.2012M511615the State Key Program of National Natural Science of China under Grant No.61134012
文摘In the literature （Tan and Wang, 2010）, Tan and Wang investigated the convergence of the split-step backward Euler （SSBE） method for linear stochastic delay integro-differential equations （SDIDEs） and proved the mean-square stability of SSBE method under some condition. Unfortu- nately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory.
文摘A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.
基金supported by National Research Foundation of Republic of Korea(Grant Nos.2011-0008976 and 2010-0011841)
文摘Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of overdetermined partial differential equations: Given a system of quasi-linear PDEs of first order for one unknown function we find a necessary and sufficient condition for the existence of solutions in terms of the second jet of the coefficients. This generalizes to certain quasi-linear systems of first order for several unknown functions.
文摘The electrohydrodynamic stability of a self-gravitating streaming compound jet has been investigated for all modes of perturbation. The jets are immersed in a dielectric motionless tenuous medium pervaded by varying electric field. A second-order integrodifferential equation of Mathieu type has been derived and some reported works are recovered as limiting cases from it.
