In this work, while applying a new and novel (G'/G)-expansion version technique, we identify four families of the traveling wave solutions to the (1 + 1)-dimensional compound KdVB equation. The exact solutions are...In this work, while applying a new and novel (G'/G)-expansion version technique, we identify four families of the traveling wave solutions to the (1 + 1)-dimensional compound KdVB equation. The exact solutions are derived, in terms of hyperbolic, trigonometric and rational functions, involving various parameters. When the parameters are tuned to special values, both solitary, and periodic wave models are distinguished. State of the art symbolic algebra graphical representations and dynamical interpretations of the obtained solutions physics are provided and discussed. This in turn ends up revealing salient solutions features and demonstrating the used method efficiency.展开更多
By using the methods of mathematics analysis, we investigate the travelling wave solution of the KdVB equation under the assumption We prove that the travelling wave solution is quantitatively similar to the correspon...By using the methods of mathematics analysis, we investigate the travelling wave solution of the KdVB equation under the assumption We prove that the travelling wave solution is quantitatively similar to the corresponding Burgers shock wave. Then we prove that the absolute error of the general asymptotic expansion is high order quantity of the small parameter展开更多
In this paper, the Fisher equation is analysed. One of its travelling wave solution is obtained by comparing it with KdV-Burgers （KdVB） equation. Its amplitude, width and speed are investigated. The instability for ...In this paper, the Fisher equation is analysed. One of its travelling wave solution is obtained by comparing it with KdV-Burgers （KdVB） equation. Its amplitude, width and speed are investigated. The instability for the higher order disturbances to the solution of the Fisher equation is also studied.展开更多
The element-free Galerkin （EFG） method for numerically solving the compound Korteweg-de Vries-Burgers （KdVB） equation is discussed in this paper. The Galerkin weak form is used to obtain the discrete equation and ...The element-free Galerkin （EFG） method for numerically solving the compound Korteweg-de Vries-Burgers （KdVB） equation is discussed in this paper. The Galerkin weak form is used to obtain the discrete equation and the essential boundary conditions are enforced by the penalty method. The effectiveness of the EFG method of solving the compound Korteweg-de Vries-Burgers （KdVB） equation is illustrated by three numerical examples.展开更多
文摘In this work, while applying a new and novel (G'/G)-expansion version technique, we identify four families of the traveling wave solutions to the (1 + 1)-dimensional compound KdVB equation. The exact solutions are derived, in terms of hyperbolic, trigonometric and rational functions, involving various parameters. When the parameters are tuned to special values, both solitary, and periodic wave models are distinguished. State of the art symbolic algebra graphical representations and dynamical interpretations of the obtained solutions physics are provided and discussed. This in turn ends up revealing salient solutions features and demonstrating the used method efficiency.
文摘By using the methods of mathematics analysis, we investigate the travelling wave solution of the KdVB equation under the assumption We prove that the travelling wave solution is quantitatively similar to the corresponding Burgers shock wave. Then we prove that the absolute error of the general asymptotic expansion is high order quantity of the small parameter
基金Project partially supported by the National Natural Science Research Foundation for the Returned 0verseas Chinese Foundation of China （Grant Nos 10575082 and 10247008）, the Scientific Scholars of State Education Ministry of China, the Natural Science Foundation of Northwest Normal University of China （Grant No NWNU-KJCXGC-215）, and the Foundation of Royal Society K C. Wong Fellowship of UK.
文摘In this paper, the Fisher equation is analysed. One of its travelling wave solution is obtained by comparing it with KdV-Burgers （KdVB） equation. Its amplitude, width and speed are investigated. The instability for the higher order disturbances to the solution of the Fisher equation is also studied.
基金Project supported by the National Natural Science Foundation of China (Grant No.10871124)the Natural Science Foundation of Zhejiang Province of China (Grant No.Y6110007)
文摘The element-free Galerkin （EFG） method for numerically solving the compound Korteweg-de Vries-Burgers （KdVB） equation is discussed in this paper. The Galerkin weak form is used to obtain the discrete equation and the essential boundary conditions are enforced by the penalty method. The effectiveness of the EFG method of solving the compound Korteweg-de Vries-Burgers （KdVB） equation is illustrated by three numerical examples.
