Based on the assumption that solute transport in a semi-infinite soil column or in a field soil profile can be described by the boundary-layer method, an analytical solution is presented for the advance of a solute fr...Based on the assumption that solute transport in a semi-infinite soil column or in a field soil profile can be described by the boundary-layer method, an analytical solution is presented for the advance of a solute front with time. The traditional convection-dispersion equation (CDE) subjected to two boundary conditions: 1) at the soil surface (or inlet boundary)and 2) at the solute front, was solved using a Laplace transformation. A comparison of resident concentrations using a boundary-layer method and an exact solution (in a semi-infinite-domain) showed that both were in good agreement within the range between the two boundaries. This led to a new method for estimating solute transport parameters in soils, requiring only observation of advance of the solute front with time. This may be corroborated visually using a tracer solution with marking-dye or measured utilizing time domain refiectometry (TDR). This method is applicable to both laboratory soil columns and field soils. Thus, it could be a step forward for modeling solute transport in field soils and for better understanding of the transport processes in soils.展开更多
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by u...Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.展开更多
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gord...By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.展开更多
基金Project supported by the National Key Basic Research Support Foundation of China (No. 2000018605) the National Natural Science Foundation of China (Nos. 40025106 and 40371060).
文摘Based on the assumption that solute transport in a semi-infinite soil column or in a field soil profile can be described by the boundary-layer method, an analytical solution is presented for the advance of a solute front with time. The traditional convection-dispersion equation (CDE) subjected to two boundary conditions: 1) at the soil surface (or inlet boundary)and 2) at the solute front, was solved using a Laplace transformation. A comparison of resident concentrations using a boundary-layer method and an exact solution (in a semi-infinite-domain) showed that both were in good agreement within the range between the two boundaries. This led to a new method for estimating solute transport parameters in soils, requiring only observation of advance of the solute front with time. This may be corroborated visually using a tracer solution with marking-dye or measured utilizing time domain refiectometry (TDR). This method is applicable to both laboratory soil columns and field soils. Thus, it could be a step forward for modeling solute transport in field soils and for better understanding of the transport processes in soils.
文摘Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.
文摘By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
