In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.展开更多
Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterativ...Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterative methods for approximating the solution of nonlinear system of equations with singular Jacobian are developed using decomposition technique. The methods proposed in this study are of convergence order , and require only the evaluation of first-order Frechet derivative per iteration. The approximate solutions generated by the proposed iterative methods in this paper compared with some existing contemporary methods in literature, show that methods developed herein are efficient and adequate in approximating the solution of nonlinear system of equations whose Jacobians are singular and non-singular at iteration points.展开更多
In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.展开更多
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic functio...By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.展开更多
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.
文摘Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterative methods for approximating the solution of nonlinear system of equations with singular Jacobian are developed using decomposition technique. The methods proposed in this study are of convergence order , and require only the evaluation of first-order Frechet derivative per iteration. The approximate solutions generated by the proposed iterative methods in this paper compared with some existing contemporary methods in literature, show that methods developed herein are efficient and adequate in approximating the solution of nonlinear system of equations whose Jacobians are singular and non-singular at iteration points.
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.
基金Project supported by the State Key Program for Basic Research of China (Grant No 2004CB418304)the National Natural Science Foundation of China (Grant No 40405010)
文摘By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.
