This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long time...This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(\epsilon\(-1)). As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(\epsilon\(-)1) are presented.展开更多
In this paper, a class of coupled system for the E1 Nifio/La Nifia southern oscillation （ENSO） atmospheric physics oscillation model is considered. We propose an ENSO atmospheric physics model using a method from th...In this paper, a class of coupled system for the E1 Nifio/La Nifia southern oscillation （ENSO） atmospheric physics oscillation model is considered. We propose an ENSO atmospheric physics model using a method from the asymptotic theory. It is indicated from the results that the asymptotic method can be used for analyzing the sea surface temperature anomaly and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model in the equatorial Pacific.展开更多
In this paper we are concerned with the integrability of the fifth Painlevé equation (PV ) from the point of view of the Hamiltonian dynamics. We prove that the PainlevéV equation (2) with parameters k∞=0,k...In this paper we are concerned with the integrability of the fifth Painlevé equation (PV ) from the point of view of the Hamiltonian dynamics. We prove that the PainlevéV equation (2) with parameters k∞=0,k0= –θ for arbitrary complex θ (and more generally with parameters related by B?clund transformations) is non integrable by means of meromorphic first integrals. We explicitly compute formal and analytic invariants of the second variational equations which generate topologically the differential Galois group. In this way our calculations and Ziglin-Ramis-Morales-Ruiz-Simó method yield to the non-integrable results.展开更多
A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a dis...A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a distribution that belongs to S（γ） with γ 〉0.展开更多
We give a brief review of the asymptotic theory of slender vortex filaments with emphases on (i) the choices of scalings and small parameters characterizing the physical problem,(ii) the key steps in the formulation o...We give a brief review of the asymptotic theory of slender vortex filaments with emphases on (i) the choices of scalings and small parameters characterizing the physical problem,(ii) the key steps in the formulation of the theory and (iii) the assumptions and/or restrictions on the theory of Callegari and Ting (1978).We present highlights of an extension of the 1978 asymptotic theory:the analyses for core structures with axial variation.Making use of the physical insights gained from the analyses,we present a new derivation of the evolution equations for the core structure.The new one is simpler and straightforward and shows the physics clearly.展开更多
The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori ...The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.展开更多
文摘This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(\epsilon\(-1)). As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(\epsilon\(-)1) are presented.
基金Project supported by the National Natural Science Foundation of China(Grant No.40876010)the Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues of the Chinese Academy of Sciences(Grant No.XDA01020304)+2 种基金the Natural Science Foundation from the Education Bureau of Anhui Province,China(Grant No.KJ2011A135)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6110502)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2011042)
文摘In this paper, a class of coupled system for the E1 Nifio/La Nifia southern oscillation （ENSO） atmospheric physics oscillation model is considered. We propose an ENSO atmospheric physics model using a method from the asymptotic theory. It is indicated from the results that the asymptotic method can be used for analyzing the sea surface temperature anomaly and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model in the equatorial Pacific.
文摘In this paper we are concerned with the integrability of the fifth Painlevé equation (PV ) from the point of view of the Hamiltonian dynamics. We prove that the PainlevéV equation (2) with parameters k∞=0,k0= –θ for arbitrary complex θ (and more generally with parameters related by B?clund transformations) is non integrable by means of meromorphic first integrals. We explicitly compute formal and analytic invariants of the second variational equations which generate topologically the differential Galois group. In this way our calculations and Ziglin-Ramis-Morales-Ruiz-Simó method yield to the non-integrable results.
基金Supported by the NNSF of China(10471076)the Science Foundation of Qufu Normal University.
文摘A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a distribution that belongs to S（γ） with γ 〉0.
文摘We give a brief review of the asymptotic theory of slender vortex filaments with emphases on (i) the choices of scalings and small parameters characterizing the physical problem,(ii) the key steps in the formulation of the theory and (iii) the assumptions and/or restrictions on the theory of Callegari and Ting (1978).We present highlights of an extension of the 1978 asymptotic theory:the analyses for core structures with axial variation.Making use of the physical insights gained from the analyses,we present a new derivation of the evolution equations for the core structure.The new one is simpler and straightforward and shows the physics clearly.
文摘The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.
