A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and im...A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and implicit or explicit based on the parameter choice. The initial value after discretization has second-order accuracy that is consistent with the scheme accuracy. The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm. Experimental results demonstrate the efficiency of the new scheme.展开更多
The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, th...The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.展开更多
We study the large time behavior of solutions of scalar conservation laws with periodic initial data. Under a very weak nonlinearity condition,we prove that the solutions converge to constants as time tends to infinit...We study the large time behavior of solutions of scalar conservation laws with periodic initial data. Under a very weak nonlinearity condition,we prove that the solutions converge to constants as time tends to infinity. Our results improve the earlier ones since we only require the flux to be nonlinear at the mean value of the initial data.展开更多
In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservat...In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given formularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.展开更多
文摘A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and implicit or explicit based on the parameter choice. The initial value after discretization has second-order accuracy that is consistent with the scheme accuracy. The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm. Experimental results demonstrate the efficiency of the new scheme.
文摘The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.
文摘We study the large time behavior of solutions of scalar conservation laws with periodic initial data. Under a very weak nonlinearity condition,we prove that the solutions converge to constants as time tends to infinity. Our results improve the earlier ones since we only require the flux to be nonlinear at the mean value of the initial data.
基金Supported by the NSF of Henan Prevince(062110300)
文摘In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given formularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.
