The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,...The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.展开更多
Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system.We define the Lie operators associated with kinetic and potential energy,and construct a n...Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system.We define the Lie operators associated with kinetic and potential energy,and construct a new kind of second order symplectic scheme,which is extremely suitable for high efficient and long-term seismic wave simulations.Three sets of optimal coefficients are obtained based on the principle of minimum truncation error.We investigate the stability conditions for elastic wave simulation in homogeneous media.These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments.One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability.The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model.展开更多
The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the...The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the variational methods, an estimate on the minimal periodof the corresponding nonconstant periodic solution of the above-mentioned system is obtained.展开更多
基金Supported partially by NSFC(11790271,12171108)Guangdong Basic and Applied Basic Research Foundation(2020A1515011019)Innovation and Development Project of Guangzhou University。
文摘The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.41174047,40874024&41204041)
文摘Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system.We define the Lie operators associated with kinetic and potential energy,and construct a new kind of second order symplectic scheme,which is extremely suitable for high efficient and long-term seismic wave simulations.Three sets of optimal coefficients are obtained based on the principle of minimum truncation error.We investigate the stability conditions for elastic wave simulation in homogeneous media.These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments.One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability.The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model.
文摘The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the variational methods, an estimate on the minimal periodof the corresponding nonconstant periodic solution of the above-mentioned system is obtained.
