In this paper,we give the complete classifications of isoparametric hypersurfaces in Randers space forms.By studying the principal curvatures of anisotropic submanifolds in a Randers space(N,F)with the navigation data...In this paper,we give the complete classifications of isoparametric hypersurfaces in Randers space forms.By studying the principal curvatures of anisotropic submanifolds in a Randers space(N,F)with the navigation data(h,W),we find that a Randers space form(N,F,dμBH)and the corresponding Riemannian space(N,h)have the same isoparametric hypersurfaces,but in general,their isoparametric functions are different.We give a necessary and sufficient condition for an isoparametric function of(N,h)to be isoparametric on(N,F,dμBH),from which we get some examples of isoparametric functions.展开更多
Combining symplectic algorithm,splitting technique and compact method,a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schr¨odinger equation with cubic-quintic nonlinear term...Combining symplectic algorithm,splitting technique and compact method,a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schr¨odinger equation with cubic-quintic nonlinear term.The scheme has fourth-order accuracy in space and second-order accuracy in time.The discrete charge conservation law and stability of the scheme are analyzed.Numerical examples are given to confirm the theoretical results.展开更多
基金Supported by NNSFC(Grant Nos.11471246 and 11971253)AHNSF(Grant No.1608085MA03)+1 种基金KLAMFJPU(Grant No.SX201805)The authors would like to thank the referees for their time and valuable comments.
文摘In this paper,we give the complete classifications of isoparametric hypersurfaces in Randers space forms.By studying the principal curvatures of anisotropic submanifolds in a Randers space(N,F)with the navigation data(h,W),we find that a Randers space form(N,F,dμBH)and the corresponding Riemannian space(N,h)have the same isoparametric hypersurfaces,but in general,their isoparametric functions are different.We give a necessary and sufficient condition for an isoparametric function of(N,h)to be isoparametric on(N,F,dμBH),from which we get some examples of isoparametric functions.
基金This work is partially supported by grants from the National Natural Science Foun-dation of China(Nos.11701196,11701197 and 11501224)the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(No.ZQN-YX502)the Key Laboratory of Applied Mathematics of Fujian Province University(Putian University)(No.SX201802).
文摘Combining symplectic algorithm,splitting technique and compact method,a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schr¨odinger equation with cubic-quintic nonlinear term.The scheme has fourth-order accuracy in space and second-order accuracy in time.The discrete charge conservation law and stability of the scheme are analyzed.Numerical examples are given to confirm the theoretical results.
