We theoretically investigate the electron localization around two nuclei in harmonic emission from asymmetric molecular ion. The results show that the ionization process of electron localized around one nucleus compet...We theoretically investigate the electron localization around two nuclei in harmonic emission from asymmetric molecular ion. The results show that the ionization process of electron localized around one nucleus competes with its transfer process to the other nucleus. By increasing the initial vibrational level, more electrons localized around the nucleus D＋ tend to transfer to the nucleus He2＋ so that the ionizations of electrons localized around the nucleus He2＋ increase. In this case, the difference in harmonic efficiency between Hell2＋ and HeD2＋ decreases while the difference in harmonic spectral structure increases. The evident minimum can be observed the spectral structure of HeD2＋, which is due to the strong in the harmonic spectrum of Hell2＋ compared with that in interference of multiple recombination channels originating from two nuclei. Time-dependent nuclear probability density, electron-nuclear probability density, double-well model, and time-frequency maps are presented to explain the underlying mechanisms.展开更多
By applying the mastersymmetry of degree one to the time-independent symmetry K_(1), the fifth-order asymmetric Nizhnik-Novikov-Veselov system is derived. The variable separation solution is obtained by using the trun...By applying the mastersymmetry of degree one to the time-independent symmetry K_(1), the fifth-order asymmetric Nizhnik-Novikov-Veselov system is derived. The variable separation solution is obtained by using the truncated Painlevé expansion with a special seed solution. New patterns of localized excitations, such as dromioff, instanton moving on a curved line, and tempo-spatial breather, are constructed. Additionally, fission or fusion solitary wave solutions are presented,graphically illustrated by several interesting examples.展开更多
Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation t...Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11404204)the Key Project of Chinese Ministry of Education(Grant No.211025)+2 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20111404120004)the Natural Science Foundation for Young Scientists of Shanxi Province,China(Grant No.2009021005)the Innovation Project for Postgraduates of Shanxi Province,China(Grant No.20133081)
文摘We theoretically investigate the electron localization around two nuclei in harmonic emission from asymmetric molecular ion. The results show that the ionization process of electron localized around one nucleus competes with its transfer process to the other nucleus. By increasing the initial vibrational level, more electrons localized around the nucleus D＋ tend to transfer to the nucleus He2＋ so that the ionizations of electrons localized around the nucleus He2＋ increase. In this case, the difference in harmonic efficiency between Hell2＋ and HeD2＋ decreases while the difference in harmonic spectral structure increases. The evident minimum can be observed the spectral structure of HeD2＋, which is due to the strong in the harmonic spectrum of Hell2＋ compared with that in interference of multiple recombination channels originating from two nuclei. Time-dependent nuclear probability density, electron-nuclear probability density, double-well model, and time-frequency maps are presented to explain the underlying mechanisms.
文摘By applying the mastersymmetry of degree one to the time-independent symmetry K_(1), the fifth-order asymmetric Nizhnik-Novikov-Veselov system is derived. The variable separation solution is obtained by using the truncated Painlevé expansion with a special seed solution. New patterns of localized excitations, such as dromioff, instanton moving on a curved line, and tempo-spatial breather, are constructed. Additionally, fission or fusion solitary wave solutions are presented,graphically illustrated by several interesting examples.
文摘Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.
