In the stratified atmosphere in which the moment nondivergent approximation was applied,introducing the nonlinear term because of the nonhomogcneous spatial distribution of density and assuming the solution to be of t...In the stratified atmosphere in which the moment nondivergent approximation was applied,introducing the nonlinear term because of the nonhomogcneous spatial distribution of density and assuming the solution to be of the form of progressive wave,we obtain a two-order nonlinear system.By means of this system,all results which were derived by Liu et al.(1984)were obtained.Moreover,it can be proved that there existed periodic solution in the nonlinear systems when there existed periodic solution in the one-order approxima- tion system,and some mathematic problems arising from series expansion were avoided.In this paper,a series of approximate solutions of nonlinear system is also discussed.展开更多
I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V...I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V is periodic in x1 with the period T>0, （V. 3） V→O, Vx→O as |x2|→∞, uniformly in （t, x1）.展开更多
It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite arra...It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.展开更多
This paper is devoted to studying the El Nino mechanism of atmospheric physics. The existence and asymptotic estimates of periodic solutions for its model are obtained by employing the technique of upper and lower sol...This paper is devoted to studying the El Nino mechanism of atmospheric physics. The existence and asymptotic estimates of periodic solutions for its model are obtained by employing the technique of upper and lower solution, and using the continuation theorem of coincidence degree theory.展开更多
In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--lo...In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a展开更多
By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric spa...By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.展开更多
文摘In the stratified atmosphere in which the moment nondivergent approximation was applied,introducing the nonlinear term because of the nonhomogcneous spatial distribution of density and assuming the solution to be of the form of progressive wave,we obtain a two-order nonlinear system.By means of this system,all results which were derived by Liu et al.(1984)were obtained.Moreover,it can be proved that there existed periodic solution in the nonlinear systems when there existed periodic solution in the one-order approxima- tion system,and some mathematic problems arising from series expansion were avoided.In this paper,a series of approximate solutions of nonlinear system is also discussed.
文摘I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V is periodic in x1 with the period T>0, （V. 3） V→O, Vx→O as |x2|→∞, uniformly in （t, x1）.
文摘It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.
基金supported by the National Natural Science Foundation of China (Grant No. 40676016)the Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK2009105 and BK2008119)+2 种基金the Natural Science Foundation of Jiangsu Education Committee, China (Grant Nos. 09kjd110001 and 08kjb110011)Key Natural Science Foundation by the Bureau of Education of Anhui Province of China (Grant No. KJ2008A05ZC)Jiangsu Teachers University of Technology Foundation (Grant No. KYY08033)
文摘This paper is devoted to studying the El Nino mechanism of atmospheric physics. The existence and asymptotic estimates of periodic solutions for its model are obtained by employing the technique of upper and lower solution, and using the continuation theorem of coincidence degree theory.
文摘In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a
文摘By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.
