The purpose of this paper is to study the long time asymptotic behavior for a nonlinear Schrdinger equations with magnetic effect. Under certain conditions, we prove the existence and nonexistence of the non-trivial f...The purpose of this paper is to study the long time asymptotic behavior for a nonlinear Schrdinger equations with magnetic effect. Under certain conditions, we prove the existence and nonexistence of the non-trivial free asymptotic solutions. In addition, the decay estimates of the solutions are also obtained.展开更多
The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding p...The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation,the convergence rates of the new profile are better than that obtained by Nishihara（1997,J.Differential Equations 137,384-395） and H.-J.Zhao（2000,J.Differential Equations 167,467-494）.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
While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approxima...While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.展开更多
The work studies the travelling wave solution of the KdV-Burgers equation. By summarizing the works in recent years, the explicit travelling wave solution is introduced.
基金Supported by the National Natural Science Foundation of China.
文摘The purpose of this paper is to study the long time asymptotic behavior for a nonlinear Schrdinger equations with magnetic effect. Under certain conditions, we prove the existence and nonexistence of the non-trivial free asymptotic solutions. In addition, the decay estimates of the solutions are also obtained.
基金National Natural Science Foundation of China(No.11301443,11171340)Specialized Research Fund for the Doctoral Program of Higher Education(No.20124301120002)+1 种基金Natural Science Foundation of Hunan Provincial(No.2015JJ3125)Scientific Research Fund of Hunan Provincial Education Department(No.13C935)
文摘The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation,the convergence rates of the new profile are better than that obtained by Nishihara（1997,J.Differential Equations 137,384-395） and H.-J.Zhao（2000,J.Differential Equations 167,467-494）.
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While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.
文摘The work studies the travelling wave solution of the KdV-Burgers equation. By summarizing the works in recent years, the explicit travelling wave solution is introduced.
