We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only ...We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only one. Secondly, a special boundary value problem of lower triangular matrix is presented and transformed into four related boundary value problems. Finally, Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials are used to give solutions.展开更多
The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plo...The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plotted well by the NRH equation at different plant growth phases due to the variations of plant development.Recently,plant physiological parameters have been considered into the NRH equation to establish the modified NRH equation,but plant height(H),an important parameter in plant growth phases,is not taken into account.In this study,H was incorporated into the NRH equation to establish the modified NRH equation,which could be used to estimate photosynthetic capability of herbage at different growth phases.To explore photosynthetic capability of herbage,we selected the dominant herbage species Potentilla anserina L.and Elymus nutans Griseb.in the Heihe River Basin,Northwest China as the research materials.Totally,twenty-four PLR curves and H at different growth phases were measured during the growing season in 2016.Results showed that the maximum net photosynthetic rate and the initial slope of PLR curve linearly increased with H.The modified NRH equation,which is established by introducing H and an H-based adjustment factor into the NRH equation,described better the PLR curves of P.anserina and E.nutans than the original ones.The results may provide an effective method to estimate the net primary productivity of grasslands in the study area.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 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
文摘We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only one. Secondly, a special boundary value problem of lower triangular matrix is presented and transformed into four related boundary value problems. Finally, Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials are used to give solutions.
基金funded by the National Natural Science Foundation of China(91025015,51178209)the Project of Arid Meteorological Science Research Foundation of China Meteorological Administration(IAM201608)
文摘The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plotted well by the NRH equation at different plant growth phases due to the variations of plant development.Recently,plant physiological parameters have been considered into the NRH equation to establish the modified NRH equation,but plant height(H),an important parameter in plant growth phases,is not taken into account.In this study,H was incorporated into the NRH equation to establish the modified NRH equation,which could be used to estimate photosynthetic capability of herbage at different growth phases.To explore photosynthetic capability of herbage,we selected the dominant herbage species Potentilla anserina L.and Elymus nutans Griseb.in the Heihe River Basin,Northwest China as the research materials.Totally,twenty-four PLR curves and H at different growth phases were measured during the growing season in 2016.Results showed that the maximum net photosynthetic rate and the initial slope of PLR curve linearly increased with H.The modified NRH equation,which is established by introducing H and an H-based adjustment factor into the NRH equation,described better the PLR curves of P.anserina and E.nutans than the original ones.The results may provide an effective method to estimate the net primary productivity of grasslands in the study area.
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.
