Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also der...Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.展开更多
The velocity tracking control of a hydraulic servo system is studied. Sincethe dynamics of the system are highly nonlinear and have large extent of model uncertainties, suchas big changes in load and parameters, a der...The velocity tracking control of a hydraulic servo system is studied. Sincethe dynamics of the system are highly nonlinear and have large extent of model uncertainties, suchas big changes in load and parameters, a derivation and integral sliding mode variable structurecontrol scheme (DI-SVSC) is proposed. An integral controller is introduced to avoid the assumptionthat the derivative of desired signal must be known in conventional sliding mode variable structurecontrol, a nonlinear derivation controller is used to weaken the chattering of system. The designmethod of switching function in integral sliding mode control, nonlinear derivation coefficient andcontrollers of DI-SVSC is presented respectively. Simulation shows that the control approach is ofnice robustness and improves velocity tracking accuracy considerably.展开更多
In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β...In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.展开更多
In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes...In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes.Therefore,it is significant to enhance the steering stability of tracked vehicle with hydrostatic drive to meet the need of future battlefield.In this paper,a sliding mode control algorithm is proposed and applied to achieve desired yaw rates.The speed controller and the yaw rate controller are designed through the kinematics and dynamics analysis.In addition,the nonlinear derivative and integral sliding mode control algorithm is designed,which is supposed to efficiently reduce the integration saturation and the disturbances from the unsmooth road surfaces through a conditional integrator approach.Moreover,it improves the response speed of the system and reduces the chattering by the derivative controller.The hydrostatic tracked vehicle module is modeled with a multi-body dynamic software RecurDyn and the steering control strategy module is modeled by MATLAB/Simulink.The co-simulation results of the whole model show that the control strategy can improve the vehicle steering response speed and also ensure a smooth control output with small chattering and strong robustness.展开更多
In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral...In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.展开更多
In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equa...In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.展开更多
The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was c...The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.展开更多
This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterization...This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.展开更多
In this paper, a fire-new general integral control, named general convex integral control, is proposed. It is derived by defining a nonlinear function set to form the integral control action and educe a new convex fun...In this paper, a fire-new general integral control, named general convex integral control, is proposed. It is derived by defining a nonlinear function set to form the integral control action and educe a new convex function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and resorting to a general strategy to transform ordinary control into general integral control. By using Lyapunov method along with the LaSalle s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the lemma to ensure the integrator output to be bounded in the time domain is proposed. The highlight point of this integral control strategy is that the integral control action seems to be infinity, but it factually is finite in the time domain. Therefore, a simple and ingenious method to design the general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole control domain of interest can all be achieved by a set of control gains, even under the case that the payload is changed abruptly.展开更多
In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm i...In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.展开更多
In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t）...In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t））dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as （x,λ） → （x0, λ0） in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]展开更多
This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorit...This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorithm and their corresponding iterated correction schemes for this kind of equations.The superconvergemceof the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammersteinintegral equations generalized to nonlinear Fredilolm equations of the second kind, but also more precise resultsare obtained by tising the wavelet method.展开更多
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison res...In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.展开更多
In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for ...In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.展开更多
In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a sy...In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.展开更多
In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of...In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method.展开更多
A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced ...A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.展开更多
In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscil...In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.展开更多
Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational ide...Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.展开更多
We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its r...We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.展开更多
基金Supported by the Natural Science Foundation of Guangdong Pronvince( 0 1 1 471 ) and Education Bu-reau( 0 1 76)
文摘Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.
文摘The velocity tracking control of a hydraulic servo system is studied. Sincethe dynamics of the system are highly nonlinear and have large extent of model uncertainties, suchas big changes in load and parameters, a derivation and integral sliding mode variable structurecontrol scheme (DI-SVSC) is proposed. An integral controller is introduced to avoid the assumptionthat the derivative of desired signal must be known in conventional sliding mode variable structurecontrol, a nonlinear derivation controller is used to weaken the chattering of system. The designmethod of switching function in integral sliding mode control, nonlinear derivation coefficient andcontrollers of DI-SVSC is presented respectively. Simulation shows that the control approach is ofnice robustness and improves velocity tracking accuracy considerably.
基金Chen research is supported by NSF of China (10961015)Yang research is supported by NSF of China (10961016)the GAN PO555 Program of Jiangxi
文摘In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.
基金Supported by the National Natural Science Foundation of China(51475044)。
文摘In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes.Therefore,it is significant to enhance the steering stability of tracked vehicle with hydrostatic drive to meet the need of future battlefield.In this paper,a sliding mode control algorithm is proposed and applied to achieve desired yaw rates.The speed controller and the yaw rate controller are designed through the kinematics and dynamics analysis.In addition,the nonlinear derivative and integral sliding mode control algorithm is designed,which is supposed to efficiently reduce the integration saturation and the disturbances from the unsmooth road surfaces through a conditional integrator approach.Moreover,it improves the response speed of the system and reduces the chattering by the derivative controller.The hydrostatic tracked vehicle module is modeled with a multi-body dynamic software RecurDyn and the steering control strategy module is modeled by MATLAB/Simulink.The co-simulation results of the whole model show that the control strategy can improve the vehicle steering response speed and also ensure a smooth control output with small chattering and strong robustness.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(Grant No.14ZB0364)
文摘In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.
文摘In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.
文摘The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.
基金The work of the author has been supported by the Deutache Forschungsgemeinschaft(DFG) under Grant Ho 1846/1-1
文摘This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
文摘In this paper, a fire-new general integral control, named general convex integral control, is proposed. It is derived by defining a nonlinear function set to form the integral control action and educe a new convex function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and resorting to a general strategy to transform ordinary control into general integral control. By using Lyapunov method along with the LaSalle s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the lemma to ensure the integrator output to be bounded in the time domain is proposed. The highlight point of this integral control strategy is that the integral control action seems to be infinity, but it factually is finite in the time domain. Therefore, a simple and ingenious method to design the general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole control domain of interest can all be achieved by a set of control gains, even under the case that the payload is changed abruptly.
文摘In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.
文摘In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t））dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as （x,λ） → （x0, λ0） in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]
文摘This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorithm and their corresponding iterated correction schemes for this kind of equations.The superconvergemceof the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammersteinintegral equations generalized to nonlinear Fredilolm equations of the second kind, but also more precise resultsare obtained by tising the wavelet method.
文摘In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
文摘In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.
文摘In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.
文摘In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method.
文摘A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.
文摘In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.
基金Supported by the Fundamental Research Funds of the Central University under Grant No. 2010LKS808the Natural Science Foundation of Shandong Province under Grant No. ZR2009AL021
文摘Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.
基金Supported by the Natural Science Foundation of China under Grant No. 60972164the Program for Liaoning Excellent Talents in University under Grant No. LJQ2011136+2 种基金the Key Technologies R&D Program of Liaoning Province under Grant No. 2011224006the Program for Liaoning Innovative Research Team in University under Grant No. LT2011019the Science and Technology Program of Shenyang under Grant No. F11-264-1-70
文摘We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.
