Because all the known integrable models possess Schwarzian forms with Mobious transformation invariance,it may be one of the best ways to find new integrable models starting from some suitable Mobious transformation i...Because all the known integrable models possess Schwarzian forms with Mobious transformation invariance,it may be one of the best ways to find new integrable models starting from some suitable Mobious transformation invariant equations. In this paper, we study the Painlevé integrability of some special (3+1)-dimensional Schwarzian models.展开更多
It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approx...It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear systems. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries （KdV） equation with a fifth-order dispersion term, the perturbed fourth-order KdV equation, the KdV-Burgers equation, and a Boussinesq-type equation.展开更多
文摘Because all the known integrable models possess Schwarzian forms with Mobious transformation invariance,it may be one of the best ways to find new integrable models starting from some suitable Mobious transformation invariant equations. In this paper, we study the Painlevé integrability of some special (3+1)-dimensional Schwarzian models.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175092)Scientific Research Fund of Zhejiang Provincial Education Department(Grant No.Y201017148)K.C.Wong Magna Fund in Ningbo University
文摘It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear systems. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries （KdV） equation with a fifth-order dispersion term, the perturbed fourth-order KdV equation, the KdV-Burgers equation, and a Boussinesq-type equation.
