A system comprised of the nonlinear Schrodinger equation coupled to the Boussinesq equation (S-B equations) which dealing with the stationary propagation of coupled non-linear upper-hybrid and magnetosonic waves in ma...A system comprised of the nonlinear Schrodinger equation coupled to the Boussinesq equation (S-B equations) which dealing with the stationary propagation of coupled non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed. To examine its solitary wave solutions, a reduced set of ordinary differential equations are considered by a simple traveling wave transformation. It is then shown that several new solutions (either functional or parametrical) can be obtained systematically, in addition to rederiving all known ones by means of our simple and direct algebra method with the help of the computer algebra system Maple.展开更多
In this study, the exact solutions for the propagation of pulses in optical fibers are obtained.Special values are given in the model used, and two nonlinear differential equations are obtained.Nonlinear equations are...In this study, the exact solutions for the propagation of pulses in optical fibers are obtained.Special values are given in the model used, and two nonlinear differential equations are obtained.Nonlinear equations are reduced to ordinary differential equations with the help of wave transformations. Then, the obtained differential equations are solved by two different methods,namely the modified simplest equation and the modified Kudryashov procedures. The solutions are given by hyperbolic, trigonometric and rational functions and the results are useful for optics,engineering and other related areas. Finally three-dimensional, contour and two-dimensional shapes are given for some solutions. These figures are important for understanding the motion of the wave. The given methods are applied to the equations for the first time. To the best of the authors' knowledge, these results are new and have not been obtained in the literature. The results are useful for applied mathematics, physics and other related areas.展开更多
基金Project supported by the Natural Science Foundation of the Education Bureau of Shaanxi Province, China (01JK119)the State Key Program of Basic Research of China (G1998030600).
文摘A system comprised of the nonlinear Schrodinger equation coupled to the Boussinesq equation (S-B equations) which dealing with the stationary propagation of coupled non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed. To examine its solitary wave solutions, a reduced set of ordinary differential equations are considered by a simple traveling wave transformation. It is then shown that several new solutions (either functional or parametrical) can be obtained systematically, in addition to rederiving all known ones by means of our simple and direct algebra method with the help of the computer algebra system Maple.
文摘In this study, the exact solutions for the propagation of pulses in optical fibers are obtained.Special values are given in the model used, and two nonlinear differential equations are obtained.Nonlinear equations are reduced to ordinary differential equations with the help of wave transformations. Then, the obtained differential equations are solved by two different methods,namely the modified simplest equation and the modified Kudryashov procedures. The solutions are given by hyperbolic, trigonometric and rational functions and the results are useful for optics,engineering and other related areas. Finally three-dimensional, contour and two-dimensional shapes are given for some solutions. These figures are important for understanding the motion of the wave. The given methods are applied to the equations for the first time. To the best of the authors' knowledge, these results are new and have not been obtained in the literature. The results are useful for applied mathematics, physics and other related areas.
