Dynamics of cubic-quintic nonlinear Schrödingeröequation are studied numerically with symplectic method. Behaviors of the equation are discussed with increased quintic nonlinear parameter. We observe homoclinic orbit crossing and elliptic orbit in turn and the system has recurrent solutions. Pattern drifting of solutions is also discussed. It is shown that pattern drifting can be slowed down by increasing the quintic nonlinear parameter.

An improved shooting method is applied to 1D Gross-Pitaevskii equation,which describes Bose-Einstein condensate of neutral atoms in harmonic trapping potential at zero temperature.Eigenvalues of ground state of condensates with different nonlinear coefficient are given.Interference of three condensates after removing the trapping potential is studied with symplectie method.A periodic evolution is shown.Influence of relative phase on interference of condensates is discussed.

Symplectic method is applied to solve numerically 1D time-dependent Gross-Pitaevskii equation. "Breathing" of the condensate is numerically illustrated. Interaction of two Bose-Einstein condensates is investigated as external potential is zero at t=0. Interference between two condensates is observed. Evolution of density due to interference at various relative phases is studied.

Interaction of multi-atom molecular ions with intense laser pulse is studied. High-order harmonic generation plateau is extended and conversion efficiency is enhanced.Physical mechanism of plateau extension is explained with classical theory.

Dynamics of one-dimensional hydrogen molecule in two-color intense laser field is studied with classical theory and symplectic algorithm.Classical trajectories are obtained by solving Hamiltonian equations numerically. Probabilities of H₂⁺,H₂²⁺,H,H⁺ are evaluated.Classical dynamics caused by laser intensity,frequency,and phase are illustrated and explained.

Classical trajectory method is used in 1D and 3D models to study classical dynamics of Hydrogen molecular ion (H₂⁺) in intense laser fields. Probabilities of survival, ionization, dissociation and Coulomb explosion and average distance between electron and the mass-center are calculated. It is shown that the 1D model is available for dynamics of hydrogen molecular ion in intense laser fields.