This paper considers the boundary stabilization and parameter estimation of a one-dimensional wave equation in the case when one end is fixed and control and harmonic disturbance with uncertain amplitude are input at ...This paper considers the boundary stabilization and parameter estimation of a one-dimensional wave equation in the case when one end is fixed and control and harmonic disturbance with uncertain amplitude are input at another end. A high-gain adaptive regulator is designed in terms of measured collocated end velocity. The existence and uniqueness of the classical solution of the closed-loop system is proven. It is shown that the state of the system approaches the standstill as time goes to infinity and meanwhile , the estimated parameter converges to the unknown parameter.展开更多
In this article, we study the string equation of type (2, 2n + 1), which is derived from 2D gravity theory or the string theory. We consider the equation as a 2n-th order analogue of the first Painlevéequation, t...In this article, we study the string equation of type (2, 2n + 1), which is derived from 2D gravity theory or the string theory. We consider the equation as a 2n-th order analogue of the first Painlevéequation, take the autonomous limit, and solve it concretely by use of the Weierstrass’ elliptic function.展开更多
Based on the Lax operator L and Orlov-Shulman's M operator,the string equations of the q-KP hierarchy are established from the special additional symmetry flows,and the negative Virasoro constraint generators {L-n...Based on the Lax operator L and Orlov-Shulman's M operator,the string equations of the q-KP hierarchy are established from the special additional symmetry flows,and the negative Virasoro constraint generators {L-n,n ≥ 1} of the 2-reduced q-KP hierarchy are also obtained.展开更多
This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is differen...This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is different completelyfrom others.展开更多
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an appl...For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.展开更多
文摘This paper considers the boundary stabilization and parameter estimation of a one-dimensional wave equation in the case when one end is fixed and control and harmonic disturbance with uncertain amplitude are input at another end. A high-gain adaptive regulator is designed in terms of measured collocated end velocity. The existence and uniqueness of the classical solution of the closed-loop system is proven. It is shown that the state of the system approaches the standstill as time goes to infinity and meanwhile , the estimated parameter converges to the unknown parameter.
文摘In this article, we study the string equation of type (2, 2n + 1), which is derived from 2D gravity theory or the string theory. We consider the equation as a 2n-th order analogue of the first Painlevéequation, take the autonomous limit, and solve it concretely by use of the Weierstrass’ elliptic function.
基金supported by the National Natural Science Foundation of China (Nos.10971109,10971209,10825101)
文摘Based on the Lax operator L and Orlov-Shulman's M operator,the string equations of the q-KP hierarchy are established from the special additional symmetry flows,and the negative Virasoro constraint generators {L-n,n ≥ 1} of the 2-reduced q-KP hierarchy are also obtained.
基金Supported in part by the NSF of China under Grant No.10671124the NCET of China under Grant No.-05-0390
文摘This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is different completelyfrom others.
基金Project supported by the Special Funds forMajor State Basic Research Projects ofChina.
文摘For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
