In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition an...We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.展开更多
A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate e...A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate expression of multiple integrals of a continuous function defined in a three-dimensional bounded domain is proposed by combining wavelet expansion and Lagrange boundary extension.Through applying such an integral technique,during the solution of nonlinear partial differential equations,the unknown function and its lower-order partial derivatives can be approximately expressed by its highest-order partial derivative values at nodes.A set of nonlinear algebraic equations with respect to these nodal values of the highest-order partial derivative is obtained using a collocation method.The validation and convergence of the proposed method are examined through several benchmark problems,including the eighth-order two-dimensional and fourth-order three-dimensional boundary value problems and the large deflection bending of von Karman plates.Results demonstrate that the present method has higher accuracy and convergence rate than most existing numerical methods.Most importantly,the convergence rate of the proposed method seems to be independent of the order of the differential equations,because it is always sixth order for second-,fourth-,sixth-,and even eighth-order problems.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.40876010the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KZCX2-YW-Q03-08+2 种基金the LASG State Key Laboratory Special Fundthe Foundation of Shanghai Municipal Education Commission under Grant No.E03004the Natural Science Foundation of Zhejiang Province under Grant No.Y6090164
文摘In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10975180, 11047025, and 11075126 and the Applied nonlinear Science and Technology from the Most Important Among all the Top Priority Disciplines of Zhejiang Province
文摘We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.
基金supported by the National Natural Science Foundation of China(Grant Nos.11925204 and 12172154)the 111 Project(Grant No.B14044)the National Key Project of China(Grant No.GJXM92579).
文摘A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate expression of multiple integrals of a continuous function defined in a three-dimensional bounded domain is proposed by combining wavelet expansion and Lagrange boundary extension.Through applying such an integral technique,during the solution of nonlinear partial differential equations,the unknown function and its lower-order partial derivatives can be approximately expressed by its highest-order partial derivative values at nodes.A set of nonlinear algebraic equations with respect to these nodal values of the highest-order partial derivative is obtained using a collocation method.The validation and convergence of the proposed method are examined through several benchmark problems,including the eighth-order two-dimensional and fourth-order three-dimensional boundary value problems and the large deflection bending of von Karman plates.Results demonstrate that the present method has higher accuracy and convergence rate than most existing numerical methods.Most importantly,the convergence rate of the proposed method seems to be independent of the order of the differential equations,because it is always sixth order for second-,fourth-,sixth-,and even eighth-order problems.
