The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values o...The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^＋ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.展开更多
15-day old seedlings of wheat and rape were grown in a series of solutions with different concentrations of KNO3 for a definite period of time. The changes in NO3- concentration of the solutions were determined by the...15-day old seedlings of wheat and rape were grown in a series of solutions with different concentrations of KNO3 for a definite period of time. The changes in NO3- concentration of the solutions were determined by the double ion-selective electrode method, and then the amount of NO3- taken up by the plants was estimated and values of Km and Imax of the Michealis-Menten equation were calculated. Results show that both the method and conditions of determination affected the values of Km and Imax. For example, the Km value was appreciably reduced when the volume of culture solution was increased or when the duration of nutrient uptake was shortened; the Km value obtained with short-term depletion method was higher than that obtained with long-term one. Similar Variations were found for the values of Imax. There was a considerable difference in the characteristics of uptake kinetics between wheat and rape when determined under the same conditions of determination. The isotherm of NO3- uptake by wheat could be separated into saturated and unsaturated parts, and when the concentration of NO3- exceeded 180 uuuuuuuuuuuuM, the relationship between the rate of NO3- uptake and NO3- concentration tended to be linear. However, the isotherm of NO3- uptake by rape was found to fit the Michealis-Menten equation and no linear relationship could be found.展开更多
The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speed...The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.展开更多
The regularization contributes to the resolution and stability in geophysical inversion. The authors apply dual-parameter shaping regularization to full waveform inversion, aiming at two points ： （ 1 ） improving th...The regularization contributes to the resolution and stability in geophysical inversion. The authors apply dual-parameter shaping regularization to full waveform inversion, aiming at two points ： （ 1 ） improving the boundary resolution, and （2） increasing convergence. Firstly, the forward modeling is done, and the inversion is processed with the optimal solution. Compared with classical Tikhonov regularization scheme, the method re fleets better resolution and stronger convergence. Then, Marmousi model is experimented and inversed, and the deep structure has a sharper outline. The phase residual comparison illustrates weaker cycle-slipping. And a choice scheme of parameter is applied in FWI.展开更多
We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition an...We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.展开更多
基金The project supported in part by the Natural Science Foundation of Education Department of Henan Province of China under Grant No. 2006110002 and the Science Foundations of Henan University of Science and Technology under Grant Nos. 2004ZD002 and 2006ZY001
文摘The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^＋ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.
文摘15-day old seedlings of wheat and rape were grown in a series of solutions with different concentrations of KNO3 for a definite period of time. The changes in NO3- concentration of the solutions were determined by the double ion-selective electrode method, and then the amount of NO3- taken up by the plants was estimated and values of Km and Imax of the Michealis-Menten equation were calculated. Results show that both the method and conditions of determination affected the values of Km and Imax. For example, the Km value was appreciably reduced when the volume of culture solution was increased or when the duration of nutrient uptake was shortened; the Km value obtained with short-term depletion method was higher than that obtained with long-term one. Similar Variations were found for the values of Imax. There was a considerable difference in the characteristics of uptake kinetics between wheat and rape when determined under the same conditions of determination. The isotherm of NO3- uptake by wheat could be separated into saturated and unsaturated parts, and when the concentration of NO3- exceeded 180 uuuuuuuuuuuuM, the relationship between the rate of NO3- uptake and NO3- concentration tended to be linear. However, the isotherm of NO3- uptake by rape was found to fit the Michealis-Menten equation and no linear relationship could be found.
文摘The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.
文摘The regularization contributes to the resolution and stability in geophysical inversion. The authors apply dual-parameter shaping regularization to full waveform inversion, aiming at two points ： （ 1 ） improving the boundary resolution, and （2） increasing convergence. Firstly, the forward modeling is done, and the inversion is processed with the optimal solution. Compared with classical Tikhonov regularization scheme, the method re fleets better resolution and stronger convergence. Then, Marmousi model is experimented and inversed, and the deep structure has a sharper outline. The phase residual comparison illustrates weaker cycle-slipping. And a choice scheme of parameter is applied in FWI.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10975180, 11047025, and 11075126 and the Applied nonlinear Science and Technology from the Most Important Among all the Top Priority Disciplines of Zhejiang Province
文摘We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.
