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 work, we apply a hyperbola function method to solve the nonlinear family of third order Korteweg-de Vries equations. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions ...In this work, we apply a hyperbola function method to solve the nonlinear family of third order Korteweg-de Vries equations. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions and trigonometric functions. The method used is a promising method to solve other nonlinear evaluation equations.展开更多
To study calculating method of settlement on top of extra-long large-diameter pile, the relevant research results were summarized. The hyperbola model, a nonlinear load transfer function, was introduced to establish t...To study calculating method of settlement on top of extra-long large-diameter pile, the relevant research results were summarized. The hyperbola model, a nonlinear load transfer function, was introduced to establish the basic differential equation with load transfer method. Assumed that the displacement of pile shaft was the high order power series of buried depth, through merging the same orthometric items and arranging the relevant coefficients, the solution which could take the nonlinear pile-soil interaction and stratum properties of soil into account was solved by power series. On the basis of the solution, by determining the load transfer depth with criterion of settlement on pile tip, the method by making boundary conditions compatible was advised to solve the load-settlement curve of pile. The relevant flow chart and mathematic expressions of boundary conditions were also listed. Lastly, the load transfer methods based on both two-broken-line model and hyperbola model were applied to analyzing a real project. The related coefficients of fitting curves by hyperbola were not less than 0.96, which shows that the hyperbola model is truthfulness, and is propitious to avoid personal error. The calculating value of load-settlement curve agrees well with the measured one, which indicates that it can be applied in engineering practice and making the theory that limits the design bearing capacity by settlement on pile top comes true.展开更多
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.
文摘In this work, we apply a hyperbola function method to solve the nonlinear family of third order Korteweg-de Vries equations. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions and trigonometric functions. The method used is a promising method to solve other nonlinear evaluation equations.
基金Project(1004178) supported by Talented Person Recommend Foundation of Changsha University of Science and Technology, China
文摘To study calculating method of settlement on top of extra-long large-diameter pile, the relevant research results were summarized. The hyperbola model, a nonlinear load transfer function, was introduced to establish the basic differential equation with load transfer method. Assumed that the displacement of pile shaft was the high order power series of buried depth, through merging the same orthometric items and arranging the relevant coefficients, the solution which could take the nonlinear pile-soil interaction and stratum properties of soil into account was solved by power series. On the basis of the solution, by determining the load transfer depth with criterion of settlement on pile tip, the method by making boundary conditions compatible was advised to solve the load-settlement curve of pile. The relevant flow chart and mathematic expressions of boundary conditions were also listed. Lastly, the load transfer methods based on both two-broken-line model and hyperbola model were applied to analyzing a real project. The related coefficients of fitting curves by hyperbola were not less than 0.96, which shows that the hyperbola model is truthfulness, and is propitious to avoid personal error. The calculating value of load-settlement curve agrees well with the measured one, which indicates that it can be applied in engineering practice and making the theory that limits the design bearing capacity by settlement on pile top comes true.
