Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to t...Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions.展开更多
We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic Bose- Einstein condensate, by linearizing the bilinear atom-molecule coupling, which allows us to conveniently probe...We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic Bose- Einstein condensate, by linearizing the bilinear atom-molecule coupling, which allows us to conveniently probe the quantum dynamics and statistics of the system. By preparing different initial states of the atomic condensate, we can observe very different quantum statistical properties of the system by exactly calculating the quadrature- squeezed and mode-correlated functions.展开更多
More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance m...More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.展开更多
In this paper,by using trapezoidal rule and the integration-by-parts formula of Malliavin calculus,we propose three new numerical schemes for solving decoupled forward-backward stochastic differential equations.We the...In this paper,by using trapezoidal rule and the integration-by-parts formula of Malliavin calculus,we propose three new numerical schemes for solving decoupled forward-backward stochastic differential equations.We theoretically prove that the schemes have second-order convergence rate.To demonstrate the effectiveness and the second-order convergence rate,numerical tests are given.展开更多
文摘Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions.
基金Supported by the National Basic Research Program of China under Grant No 2007CB307002, the National Natural Science Foundation of China under Grant Nos 10334010 and 10304020, the PCSIRT, the 111 Project （B07013）, Key International ST Cooperation Project under Grant No 2005DFA10170, the Cultivation Fund of the Key Scientific and Technical Innovation Project, the Ministry of Education of China under Grant No 704012, and the Wuhan Youth Chen-Guang Programme.
文摘We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic Bose- Einstein condensate, by linearizing the bilinear atom-molecule coupling, which allows us to conveniently probe the quantum dynamics and statistics of the system. By preparing different initial states of the atomic condensate, we can observe very different quantum statistical properties of the system by exactly calculating the quadrature- squeezed and mode-correlated functions.
文摘More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.
基金supported by National Natural Science Foundation of China (Grant Nos. 91130003 and 11171189)Natural Science Foundation of Shandong Province (Grant No. ZR2011AZ002)
文摘In this paper,by using trapezoidal rule and the integration-by-parts formula of Malliavin calculus,we propose three new numerical schemes for solving decoupled forward-backward stochastic differential equations.We theoretically prove that the schemes have second-order convergence rate.To demonstrate the effectiveness and the second-order convergence rate,numerical tests are given.
