The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie gr...The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.展开更多
基金supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institutethe National Natural Science Foundation of China under Grant Nos. 10735030 and 90503006
文摘The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
