Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric d...Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.展开更多
By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation th...By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.展开更多
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Ko...By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.展开更多
In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated ...In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.展开更多
基金＊Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
文摘Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10735030, 90718041, and 40975038Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)
文摘By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.
基金Supported by National Natural Science Foundation of China under Grant No.71171035
文摘By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
文摘In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.
