In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equ...SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.展开更多
Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fer...Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of AblowRz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.展开更多
By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients,...By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.展开更多
A variable coefficient, rotation-modified extended Kortweg-deVries （vReKdV） model is applied to the study of the South China Sea （SCS）, with focus on the effects of the high-order （cubic） nonlinearity and the ro...A variable coefficient, rotation-modified extended Kortweg-deVries （vReKdV） model is applied to the study of the South China Sea （SCS）, with focus on the effects of the high-order （cubic） nonlinearity and the rotation on the disintegration process of large-amplitude （170 m） Internal Solitary Waves （ISWs） and the semi-diurnal internal tide propagating from the deep basin station to the slope and shelf regions in a continuously stratified system. The numerical solutions show that the high-order nonlinearity significantly affects the wave profile by increasing the wave amplitude and the phase speed in the simulated area. It is shown that the initial KdV-type ISW will decay faster when the rotation dispersion is considered, however the wave profile does not change significantly and the rotation effect is not important. The simulations of the semi-diurnal internal tide indicate that the phase of the wave profile is shifted earlier when the rotation effect is included. A solitary wave packet emerges on the shelf, and the wave speed is also greater when considering the rotation dispersion. In addition, the effects of the background currents are discussed further in this paper It is found that the background currents generally change the magnitude and occasionally change the sign of the nonlinear coefficients in the northern SCS.展开更多
The generalized sub-ODE method, the rational （G＇/G）-expansion method, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential ...The generalized sub-ODE method, the rational （G＇/G）-expansion method, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations （PDEs）. Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV （GKdV-mKdV） equation with higherorder nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.展开更多
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
基金supported by the National Natural Science Foundation of China (Grant No. 50921001)
文摘SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.
文摘Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of AblowRz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.
基金Project supported by the National Natural Science Foundation of China (Grant No.10735030)Natural Science Foundation of Zhejiang Province of China (Grant No.Y6090592)+1 种基金Natural Science Foundation of Ningbo City (Grant No.2008A610017)K.C.Wong Magna Fund in Ningbo University
文摘By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.
基金supported by the National Natural Science Foundation of China(Grant No.41030855)
文摘A variable coefficient, rotation-modified extended Kortweg-deVries （vReKdV） model is applied to the study of the South China Sea （SCS）, with focus on the effects of the high-order （cubic） nonlinearity and the rotation on the disintegration process of large-amplitude （170 m） Internal Solitary Waves （ISWs） and the semi-diurnal internal tide propagating from the deep basin station to the slope and shelf regions in a continuously stratified system. The numerical solutions show that the high-order nonlinearity significantly affects the wave profile by increasing the wave amplitude and the phase speed in the simulated area. It is shown that the initial KdV-type ISW will decay faster when the rotation dispersion is considered, however the wave profile does not change significantly and the rotation effect is not important. The simulations of the semi-diurnal internal tide indicate that the phase of the wave profile is shifted earlier when the rotation effect is included. A solitary wave packet emerges on the shelf, and the wave speed is also greater when considering the rotation dispersion. In addition, the effects of the background currents are discussed further in this paper It is found that the background currents generally change the magnitude and occasionally change the sign of the nonlinear coefficients in the northern SCS.
文摘The generalized sub-ODE method, the rational （G＇/G）-expansion method, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations （PDEs）. Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV （GKdV-mKdV） equation with higherorder nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.
