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
In this paper, a new transformation is introduced to solve triple sine-Gordon equation. It is shown that this intermediate transformation method is powerful to solve complex special type nonlinear evolution equation.
Segmental perforation is widely used for horizontal wells. However,the flow of fluid in porous media is a complex problem. Using the Fourier transform,principle of potential superposition,trigonometric function transf...Segmental perforation is widely used for horizontal wells. However,the flow of fluid in porous media is a complex problem. Using the Fourier transform,principle of potential superposition,trigonometric function transform,asymptotic analyses,a pressure solution of a pseudo steady-state flow model in 3D circular-boxed media has been established. Comparing with the productivity of vertical wells,an equivalence radius model can be obtained. Based on the model,a method of evaluating the productivity of segmental perforation horizontal well is presented by means of principle of superposition. It shows that the equivalence radius is different for various positions of horizontal wells; the output of both ends of horizontal wells is greater than the others under the same length of perforation interval; it is more important to obtain high productivity by increasing the length of perforation interval than enlarging the spacing between perforation intervals. The result of this research can be used to ascertain the yield of each perforated interval.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.
文摘In this paper, a new transformation is introduced to solve triple sine-Gordon equation. It is shown that this intermediate transformation method is powerful to solve complex special type nonlinear evolution equation.
基金supported by the China National 973 Program (Grant No. 2003CB214602)
文摘Segmental perforation is widely used for horizontal wells. However,the flow of fluid in porous media is a complex problem. Using the Fourier transform,principle of potential superposition,trigonometric function transform,asymptotic analyses,a pressure solution of a pseudo steady-state flow model in 3D circular-boxed media has been established. Comparing with the productivity of vertical wells,an equivalence radius model can be obtained. Based on the model,a method of evaluating the productivity of segmental perforation horizontal well is presented by means of principle of superposition. It shows that the equivalence radius is different for various positions of horizontal wells; the output of both ends of horizontal wells is greater than the others under the same length of perforation interval; it is more important to obtain high productivity by increasing the length of perforation interval than enlarging the spacing between perforation intervals. The result of this research can be used to ascertain the yield of each perforated interval.
