Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equati...Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.展开更多
Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and m...Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and more new kinds of solitary wave solutions are obtained.展开更多
Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave soluti...Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave solutions of certain nonlinear partial differential models.Now we can further extend the new algorithm to other nonlinear differential-different models.展开更多
An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be f...An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.展开更多
In this paper, new Jacobi elliptic function solutions of multi-component mKdV equation are obtained directly in a unified way. When the modulus m → 1, those periodic solutions degenerate as the corresponding hyperbol...In this paper, new Jacobi elliptic function solutions of multi-component mKdV equation are obtained directly in a unified way. When the modulus m → 1, those periodic solutions degenerate as the corresponding hyperbolic function solutions. Then, to the three-component mKdV equation, five types of effective solution are presented in detail.展开更多
The aim of this study was to assess the runoff amount from a catchment characterized by diverse land uses by using the Soil Conservation Service Curve Number(SCS-CN) method based on Curve Number(CN) defined for domina...The aim of this study was to assess the runoff amount from a catchment characterized by diverse land uses by using the Soil Conservation Service Curve Number(SCS-CN) method based on Curve Number(CN) defined for dominant homogeneous elementary sub-regions.The calculations employed the SCS-CN method,involving the division of the catchment in two homogeneous parts and determining the runoff amount.The obtained results were compared with the results provided by three other CN determination methods,i.e.the Hawkins function,the kinetics equation,and a complementary error function peak.The catchment is located in a mountain dominated by forest land cover.Empirical CN-Precipitation(CN_(emp)-P) data pairs were analyzed using the mentioned methods,and the highest quality score was achieved from model 1.The results suggest that dividing a catchment into two homogeneous areas and determining their separate CN parameters,used later on to calculate the runoff by means of the presented approach,could be an alternative to the standard methods.The described method is relatively easy,and as it does not require an adoption of numerous parameters,and it can be employed for designing hydraulic facilities.展开更多
文摘Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
基金The project supported by National Natural Science Foundation of China under Grant Nos.40045016 and 40175016
文摘Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and more new kinds of solitary wave solutions are obtained.
文摘Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave solutions of certain nonlinear partial differential models.Now we can further extend the new algorithm to other nonlinear differential-different models.
文摘An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.
基金The project supported by the Education Foundation of Zhejiang Province of China under Grant No. 20030557 and the Science Foundation of Zhejiang Forestry College
文摘In this paper, new Jacobi elliptic function solutions of multi-component mKdV equation are obtained directly in a unified way. When the modulus m → 1, those periodic solutions degenerate as the corresponding hyperbolic function solutions. Then, to the three-component mKdV equation, five types of effective solution are presented in detail.
基金Dean of the Faculty of Environmental Engineering and Land Surveying, University of Agriculture in Krakow, for financial support
文摘The aim of this study was to assess the runoff amount from a catchment characterized by diverse land uses by using the Soil Conservation Service Curve Number(SCS-CN) method based on Curve Number(CN) defined for dominant homogeneous elementary sub-regions.The calculations employed the SCS-CN method,involving the division of the catchment in two homogeneous parts and determining the runoff amount.The obtained results were compared with the results provided by three other CN determination methods,i.e.the Hawkins function,the kinetics equation,and a complementary error function peak.The catchment is located in a mountain dominated by forest land cover.Empirical CN-Precipitation(CN_(emp)-P) data pairs were analyzed using the mentioned methods,and the highest quality score was achieved from model 1.The results suggest that dividing a catchment into two homogeneous areas and determining their separate CN parameters,used later on to calculate the runoff by means of the presented approach,could be an alternative to the standard methods.The described method is relatively easy,and as it does not require an adoption of numerous parameters,and it can be employed for designing hydraulic facilities.
