An immobilized Cu2O/g-C3N4 heterojunction film was successfully made on an FTO substrate by electrophoretic deposition of g-C3N4 on a Cu2O thin film.The photoelectrochemical（PEC） performance for water splitting by t...An immobilized Cu2O/g-C3N4 heterojunction film was successfully made on an FTO substrate by electrophoretic deposition of g-C3N4 on a Cu2O thin film.The photoelectrochemical（PEC） performance for water splitting by the Cu2O/g-C3N4 film was better than pure g-C3N4 and pure Cu2O film.Under-0.4 V external bias and visible light irradiation,the photocurrent density and PEC hydrogen evolution efficiency of the optimized Cu2O/g-C3N4 film was-1.38 mA/cm^2 and 0.48 mL h^-1 cm^-2,respectively.The enhanced PEC performance of Cu2O/g-C3N4 was attributed to the synergistic effect of light coupling and a matching energy band structure between g-C3N4 and Cu2O as well as the external bias.展开更多
Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function,...Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice.展开更多
In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the repr...In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.展开更多
Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamilto...Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differentiM equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable ease of the two-dimensional Hamiltonian system.展开更多
The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary paramete...The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.展开更多
Starting from the subgroups of the group U（n）, the corresponding Lie algebras of the Lie algebra Al are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few exp...Starting from the subgroups of the group U（n）, the corresponding Lie algebras of the Lie algebra Al are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given.展开更多
In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal sys...In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.展开更多
In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKN...In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.展开更多
基金supported by the National Natural Science Foundation of China (21173088)the Science and Technology Project of Guangdong Province (2014A030312007, 2015A050502012, 2016A010104013)+1 种基金the China Postdoctoral Science Foundation (2016M592493)the Open Research Fund of Hunan Key Laboratory of Applied Environmental Photocatalysis (CCSU-XT-06),Changsha University~~
文摘An immobilized Cu2O/g-C3N4 heterojunction film was successfully made on an FTO substrate by electrophoretic deposition of g-C3N4 on a Cu2O thin film.The photoelectrochemical（PEC） performance for water splitting by the Cu2O/g-C3N4 film was better than pure g-C3N4 and pure Cu2O film.Under-0.4 V external bias and visible light irradiation,the photocurrent density and PEC hydrogen evolution efficiency of the optimized Cu2O/g-C3N4 film was-1.38 mA/cm^2 and 0.48 mL h^-1 cm^-2,respectively.The enhanced PEC performance of Cu2O/g-C3N4 was attributed to the synergistic effect of light coupling and a matching energy band structure between g-C3N4 and Cu2O as well as the external bias.
文摘Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice.
文摘In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.
基金the Funds for Basic Research Project under Grant Nos.06XJC033 and 2008Bl10003
文摘Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differentiM equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable ease of the two-dimensional Hamiltonian system.
文摘The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.
基金The project supported by National Natural Science Foundation of China under Grant No. 10471139 and Hong Kong Research Grant Council under Grant No. HKBU RGC 2016/05p
文摘Starting from the subgroups of the group U（n）, the corresponding Lie algebras of the Lie algebra Al are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given.
文摘In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.
基金Supported by the National Natural Science Foundation of China under Grant No.10926036the Education Department of Zhejiang Province under Grant No.Y200906909the Zhejiang Provincial Natural Science Foundation of China under Grant No.Y6090172
文摘In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.
