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
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
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
In this paper, the quantum hydrodynamics (QHD) model is used to study the propagation of small- but finite-amplitude quantum electrostatic shock-wave in an inertial-less symmetric pair (ion) plasma with immobile backg...In this paper, the quantum hydrodynamics (QHD) model is used to study the propagation of small- but finite-amplitude quantum electrostatic shock-wave in an inertial-less symmetric pair (ion) plasma with immobile background positive constituents. The dispersion due to the quantum tunneling and inertial effects as well as dissipation caused by particle collisions leading to the shock-like or double-layer structures are considered. Investigation of both the stationary and traveling-wave solutions to Kortewege-de Veries-Burgers evolution equation show that critical values exist which govern the type of collective plasma structures. Current analysis apply to diverse kind of symmetric plasmas such as laboratory inertially confined or astrophysical pair-ion or electron-positron degenerate plasmas.展开更多
The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi m...The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger （dKdVB） equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar （cylindrical and spherical） geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.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.
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.
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.
文摘In this paper, the quantum hydrodynamics (QHD) model is used to study the propagation of small- but finite-amplitude quantum electrostatic shock-wave in an inertial-less symmetric pair (ion) plasma with immobile background positive constituents. The dispersion due to the quantum tunneling and inertial effects as well as dissipation caused by particle collisions leading to the shock-like or double-layer structures are considered. Investigation of both the stationary and traveling-wave solutions to Kortewege-de Veries-Burgers evolution equation show that critical values exist which govern the type of collective plasma structures. Current analysis apply to diverse kind of symmetric plasmas such as laboratory inertially confined or astrophysical pair-ion or electron-positron degenerate plasmas.
基金Supported by Quaid-i-Azam University Research Fund,URF Project No.URF/(2007-2009)
文摘The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger （dKdVB） equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar （cylindrical and spherical） geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.
