One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then...One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then by choosing the eigenfunctions of the linear operator as bases, the Hamiltonian system in the coordinates is expressed. Because of the intricate resonance between the tangential frequencies and normal frequencies, some quasi-periodic solutions with special structures are considered. Secondly, the regularity of the Hamiltonian vector field is verified and then the fourth-order terms are normalized. By the Birkhoff normal form, the non- degeneracy and non-resonance conditions are obtained. Applying the infinite dimensional Kolmogorov-Arnold-Moser （KAM） theorem, the existence of finite dimensional invariant tori for the equivalent Hamiltonian system is proved. Hence many small-amplitude quasi-periodic solutions for the above equation are obtained.展开更多
The CS radical was generated by discharging the mixture gas of CS2 and Helium. The Doppler limited spectra of CS were recorded in the region of 12350-12950 cm^-1 using optical heterodyne concentration modulation absor...The CS radical was generated by discharging the mixture gas of CS2 and Helium. The Doppler limited spectra of CS were recorded in the region of 12350-12950 cm^-1 using optical heterodyne concentration modulation absorption spectroscopy. Three hundred and twenty-six lines were recorded and assigned to the d^3△-a^3П （8,1） band, in which eighty-three transitions were first observed. A set of improved molecular constants for the d^3△（v=8） and a^3П（v=1） levels were determined by a non-linear least-squares fitting of all the lines to the effective Hamiltonian.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
基金The National Natural Science Foundation of China(No.11301072)the Natural Science Foundation of Jiangsu Province(No.BK20131285)the Research and Innovation Project for College Graduates of Jiangsu Province(No.CXZZ12-0083,CXLX13-074)
文摘One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then by choosing the eigenfunctions of the linear operator as bases, the Hamiltonian system in the coordinates is expressed. Because of the intricate resonance between the tangential frequencies and normal frequencies, some quasi-periodic solutions with special structures are considered. Secondly, the regularity of the Hamiltonian vector field is verified and then the fourth-order terms are normalized. By the Birkhoff normal form, the non- degeneracy and non-resonance conditions are obtained. Applying the infinite dimensional Kolmogorov-Arnold-Moser （KAM） theorem, the existence of finite dimensional invariant tori for the equivalent Hamiltonian system is proved. Hence many small-amplitude quasi-periodic solutions for the above equation are obtained.
文摘The CS radical was generated by discharging the mixture gas of CS2 and Helium. The Doppler limited spectra of CS were recorded in the region of 12350-12950 cm^-1 using optical heterodyne concentration modulation absorption spectroscopy. Three hundred and twenty-six lines were recorded and assigned to the d^3△-a^3П （8,1） band, in which eighty-three transitions were first observed. A set of improved molecular constants for the d^3△（v=8） and a^3П（v=1） levels were determined by a non-linear least-squares fitting of all the lines to the effective Hamiltonian.
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.
