A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissma...A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme,we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations(PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.展开更多
In this paper, an improved element-free Galerkin （IEFG） method is proposed to solve the generalized fifth-order Korteweg-de Vries （gfKdV） equation. When the traditional element-free Galerkin （EFG） method is used...In this paper, an improved element-free Galerkin （IEFG） method is proposed to solve the generalized fifth-order Korteweg-de Vries （gfKdV） equation. When the traditional element-free Galerkin （EFG） method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares （MLS） shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares （IMLS） approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method.展开更多
The Schamel–Korteweg–de Vries equation is investigated by the approach of dynamics.The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behavi...The Schamel–Korteweg–de Vries equation is investigated by the approach of dynamics.The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behaviors with phase space analyses.The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given.All possible exact explicit parametric representations of the waves are also presented.Along with the details of the analyses,the analytical results are numerically simulated lastly.展开更多
基金Project supported by the Program for Innovative Research Team in Science and Technology in Fujian Province University,China,the Quanzhou High Level Talents Support Plan,China(Grant No.2017ZT012)the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University,China(Grant No.ZQN-YX502)
文摘A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme,we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations(PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.
基金the National Basic Research Program of China(Grant No.2012CB025903)
文摘In this paper, an improved element-free Galerkin （IEFG） method is proposed to solve the generalized fifth-order Korteweg-de Vries （gfKdV） equation. When the traditional element-free Galerkin （EFG） method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares （MLS） shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares （IMLS） approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method.
基金supported by the National Natural Science Foundation of China (Grant No.11461022)。
文摘The Schamel–Korteweg–de Vries equation is investigated by the approach of dynamics.The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behaviors with phase space analyses.The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given.All possible exact explicit parametric representations of the waves are also presented.Along with the details of the analyses,the analytical results are numerically simulated lastly.
