In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the syst...In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.展开更多
Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging me...Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure.展开更多
In this paper, the KP-MEW(2,2) equation is considered under a certain parametric condition. We prove that the equation has two isochronous centers under certain parametric conditions, and there exist two families of p...In this paper, the KP-MEW(2,2) equation is considered under a certain parametric condition. We prove that the equation has two isochronous centers under certain parametric conditions, and there exist two families of periodic solutions with equal period.展开更多
An upper bound B(n)≤ 12{7n+12((-1) n-1)} is derived for the number of zeros of Abelian integralsI(h)=∮ Γ h g(x,y)dy-f(x,y)dx on the open interval (-112,0)∪ (0,+∞), where Γ h is the...An upper bound B(n)≤ 12{7n+12((-1) n-1)} is derived for the number of zeros of Abelian integralsI(h)=∮ Γ h g(x,y)dy-f(x,y)dx on the open interval (-112,0)∪ (0,+∞), where Γ h is the compact component of the algebraic curve H(x,y)=12y 2+13x 3+14x 4=h,f(x,y) and g(x,y) are polynomials of x and y,n= max s{ deg f(x,y), deg g(x,y)} .展开更多
The parametric representation for finite-band solutions of a stationary soliton equation is discussed. This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense. ...The parametric representation for finite-band solutions of a stationary soliton equation is discussed. This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense. The nonconfocal involutive integral representations {Fm} are obtained also The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.展开更多
In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochas...In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger equations.It is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete energy.Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.展开更多
文摘In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.
基金The project supported by the Post-Doctoral Foundation of China
文摘Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure.
文摘In this paper, the KP-MEW(2,2) equation is considered under a certain parametric condition. We prove that the equation has two isochronous centers under certain parametric conditions, and there exist two families of periodic solutions with equal period.
文摘An upper bound B(n)≤ 12{7n+12((-1) n-1)} is derived for the number of zeros of Abelian integralsI(h)=∮ Γ h g(x,y)dy-f(x,y)dx on the open interval (-112,0)∪ (0,+∞), where Γ h is the compact component of the algebraic curve H(x,y)=12y 2+13x 3+14x 4=h,f(x,y) and g(x,y) are polynomials of x and y,n= max s{ deg f(x,y), deg g(x,y)} .
基金the National Natural Science Fundation of China (No.10071097).
文摘The parametric representation for finite-band solutions of a stationary soliton equation is discussed. This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense. The nonconfocal involutive integral representations {Fm} are obtained also The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.
基金supported by the NNSFC(No.11001009)supported by the Director Foundation of GUCAS,the NNSFC(No.11071251)supported by the Foundation of CAS and the NNSFC(No.11021101,No.91130003).
文摘In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger equations.It is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete energy.Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.
