The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth so...The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented.展开更多
This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorr...This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorrect result.By computing the geometric error directly without accumulating the approximation error and chord error,the authors realize correct geometric error control by establishing inequality constraints on the accelerations of the motion.展开更多
A new algorithm for the stabilization or (possibly turbulent, chaotic) distributed systems,governed by linear or non linear systems of equations is presented.The SPA (Stabilization Parallel Algorithm) is based on a sy...A new algorithm for the stabilization or (possibly turbulent, chaotic) distributed systems,governed by linear or non linear systems of equations is presented.The SPA (Stabilization Parallel Algorithm) is based on a systematic parallel decompositionof the problem (related to arbitrarily overlapping decomposition of domains) and on a penaltyargument.SPA is presented here for the case of linear parabolic equations, with distributed or boundarycontrol. It extends to practically all linear and non linear evolution equations, as it will bepresented in several other publications.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.11461022the Major Natural Science Foundation of Yunnan Province under Grant No.2014FA037
文摘The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented.
基金supported partially by the National Natural Science Foundation of China under Grant Nos.10871195 and 60821002/F02National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences
文摘This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorrect result.By computing the geometric error directly without accumulating the approximation error and chord error,the authors realize correct geometric error control by establishing inequality constraints on the accelerations of the motion.
文摘A new algorithm for the stabilization or (possibly turbulent, chaotic) distributed systems,governed by linear or non linear systems of equations is presented.The SPA (Stabilization Parallel Algorithm) is based on a systematic parallel decompositionof the problem (related to arbitrarily overlapping decomposition of domains) and on a penaltyargument.SPA is presented here for the case of linear parabolic equations, with distributed or boundarycontrol. It extends to practically all linear and non linear evolution equations, as it will bepresented in several other publications.
