The Hirota-Satsuma coupled KdV equations associated 2 x 2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra ...The Hirota-Satsuma coupled KdV equations associated 2 x 2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator.展开更多
We study the coupled mKdV equation by the dressing method via local Riemann-Hilbert problem. With the help of the Lax pairs, we obtain the matrix Riemann-Hilbert problem with zeros. The explicit solutions for the coup...We study the coupled mKdV equation by the dressing method via local Riemann-Hilbert problem. With the help of the Lax pairs, we obtain the matrix Riemann-Hilbert problem with zeros. The explicit solutions for the coupled mKdV equation are derived with the aid of the regularization of the Riemann-Hilbert problem.展开更多
A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(...A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(γA,σB)matrix KP hierarchy are studied.The dressing method is generalized to the(γA,σB)-matrix KP hierarchy and some solutions are presented.展开更多
In this paper, a new integrable variable coefficient Toda equation is proposed by utilizing a generalized version of the dressing method. At the same time, we derive the Lax pair of the new integrable variable coeffic...In this paper, a new integrable variable coefficient Toda equation is proposed by utilizing a generalized version of the dressing method. At the same time, we derive the Lax pair of the new integrable variable coefficient Toda equation. The compatibility condition is given, which insures that the new Toda equation is integrable. To further analyze the character of the Toda equation, we derive one soliton solution of the obtained Toda equation by using separation of variables.展开更多
We propose schemes to realize quantum state transfer and prepare quantum entanglement in coupled cavity and cavity-fiber-cavity systems,respectively,by using the dressed state method.We first give the expression of pu...We propose schemes to realize quantum state transfer and prepare quantum entanglement in coupled cavity and cavity-fiber-cavity systems,respectively,by using the dressed state method.We first give the expression of pulses shape by using dressed states and then find a group of Gaussian pulses that are easy to realize in experiment to replace the ideal pulses by curve fitting.We also study the influence of some parameters fluctuation,atomic spontaneous emission,and photon leakage on fidelity.The results show that our schemes have good robustness.Because the atoms are trapped in different cavities,it is easy to perform different operations on different atoms.The proposed schemes have the potential applications in dressed states for distributed quantum information processing tasks.展开更多
Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reduct...Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.11001250
文摘The Hirota-Satsuma coupled KdV equations associated 2 x 2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator.
文摘We study the coupled mKdV equation by the dressing method via local Riemann-Hilbert problem. With the help of the Lax pairs, we obtain the matrix Riemann-Hilbert problem with zeros. The explicit solutions for the coupled mKdV equation are derived with the aid of the regularization of the Riemann-Hilbert problem.
基金Supported by the National Science Foundation of China under Grant Nos. 10801083,10901090,11171175China Postdoctoral Science Funded Project (20110490408)Chinese Universities Scientific Fund under Grant No. 2011JS041
文摘A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(γA,σB)matrix KP hierarchy are studied.The dressing method is generalized to the(γA,σB)-matrix KP hierarchy and some solutions are presented.
文摘In this paper, a new integrable variable coefficient Toda equation is proposed by utilizing a generalized version of the dressing method. At the same time, we derive the Lax pair of the new integrable variable coefficient Toda equation. The compatibility condition is given, which insures that the new Toda equation is integrable. To further analyze the character of the Toda equation, we derive one soliton solution of the obtained Toda equation by using separation of variables.
基金Project supported by the National Natural Science Foundation of China(Grant No.11804308).
文摘We propose schemes to realize quantum state transfer and prepare quantum entanglement in coupled cavity and cavity-fiber-cavity systems,respectively,by using the dressed state method.We first give the expression of pulses shape by using dressed states and then find a group of Gaussian pulses that are easy to realize in experiment to replace the ideal pulses by curve fitting.We also study the influence of some parameters fluctuation,atomic spontaneous emission,and photon leakage on fidelity.The results show that our schemes have good robustness.Because the atoms are trapped in different cavities,it is easy to perform different operations on different atoms.The proposed schemes have the potential applications in dressed states for distributed quantum information processing tasks.
基金Supported by a grant from City University of Hong Kong(Project No:7002366)the support by National Natural Science Foundation of China(Project No:11301149)+1 种基金Henan Natural Science Foundation For Basic Research under Grant No:132300410310Doctor Foundation of Henan Institute of Engeering under Grant No:D2010007
文摘Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed.
