In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik...In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equations are obtained. It is shown that the new method is much more powerful in finding new exact solutions to various kinds of nonlinear evolution equations in mathematical physics.展开更多
In this paper,we present a generalized Jacobi spectral Galerkin method for fractional Volterra integro-differential equations(FVIDEs).The basis functions of the proposed method are generalized Jacobi functions,which s...In this paper,we present a generalized Jacobi spectral Galerkin method for fractional Volterra integro-differential equations(FVIDEs).The basis functions of the proposed method are generalized Jacobi functions,which serve as natural basis functions for appropriately designed spectral methods for FVIDEs.We establish a convergence analysis of the generalized Jacobi spectral Galerkin method under reasonable assumptions.Numerical experiments are provided to demonstrate the effectiveness of the proposed method.展开更多
In this paper, based on the generalized Jacobi elliptic function expansion method, we obtain abundant new explicit and exact solutions of the Klein-Gordon- Zakharov equations, which degenerate to solitary wave solutio...In this paper, based on the generalized Jacobi elliptic function expansion method, we obtain abundant new explicit and exact solutions of the Klein-Gordon- Zakharov equations, which degenerate to solitary wave solutions and triangle function solutions in the limit cases, showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations in mathematical physics.展开更多
基金The Scientific Research Foundation (QKJA2010011) of Nanjing Institute of Technology
文摘In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equations are obtained. It is shown that the new method is much more powerful in finding new exact solutions to various kinds of nonlinear evolution equations in mathematical physics.
基金supported by the Visiting Scholar Program of the National Natural Science Foundation of China(Grant No.12426616)the Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications(Grant No.NY223127).
文摘In this paper,we present a generalized Jacobi spectral Galerkin method for fractional Volterra integro-differential equations(FVIDEs).The basis functions of the proposed method are generalized Jacobi functions,which serve as natural basis functions for appropriately designed spectral methods for FVIDEs.We establish a convergence analysis of the generalized Jacobi spectral Galerkin method under reasonable assumptions.Numerical experiments are provided to demonstrate the effectiveness of the proposed method.
基金The Scientific Research Foundation (KXJ08047) of NanJing Institute of Technology
文摘In this paper, based on the generalized Jacobi elliptic function expansion method, we obtain abundant new explicit and exact solutions of the Klein-Gordon- Zakharov equations, which degenerate to solitary wave solutions and triangle function solutions in the limit cases, showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations in mathematical physics.
