To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of t...To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of the elements of a new loop algebra which is obtained by using perturbation method. Therefore, the approach given in the paper has extensive applicable values, that is, it applies to investigate a lot of double integrable couplings of the known integrable hierarchies of evolution equations. As for explicit applications of the method proposed in the paper, the double integrable couplings of the AKNS hierarchy and the KN hierarchy are worked out, respectively.展开更多
It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel so...It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.展开更多
In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmeth...In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.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
The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which availab...The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected. Then, a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices. The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and auto-correlation with the natural frequency of the plaintext being hidden and homogenized.展开更多
The assumption of static and deterministic conditions is common in the practice of construction project planning. However, at the construction phase, projects are subject to uncertainty. This may lead to serious sched...The assumption of static and deterministic conditions is common in the practice of construction project planning. However, at the construction phase, projects are subject to uncertainty. This may lead to serious schedule disruptions and, as a consequence, serious revisions oft.he schedule baseline. The aim of the paper is developing a method for constructing robust project schedules with a proactive procedure. Robust project scheduling allows for constructing stable schedules with time buffers introduced to cope with multiple disruptions during project execution. The method proposed by the authors, based on Monte Carlo simulation technique and mathematical programming for buffer sizing optimization, was applied to scheduling an example project. The results were compared, in terms of schedule stability, to those of the float factor heuristic procedttre.展开更多
In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and fo...In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto(GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective,reliable and does not require any restrictive assumptions for nonlinear terms.展开更多
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ...Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10971031
文摘To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of the elements of a new loop algebra which is obtained by using perturbation method. Therefore, the approach given in the paper has extensive applicable values, that is, it applies to investigate a lot of double integrable couplings of the known integrable hierarchies of evolution equations. As for explicit applications of the method proposed in the paper, the double integrable couplings of the AKNS hierarchy and the KN hierarchy are worked out, respectively.
基金supported by the Research Work of Liaoning Provincial Development of Education under Grant No. 2008670
文摘It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.
基金Supported by the National Natural Science Foundation of China under Grant No. 10735030Shanghai Leading Academic Discipline Project under Grant No. B412+2 种基金National Natural Science Foundation of China under Grant No. 90718041Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0734K.C. Wong Magna Fund in Ningbo University
文摘In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.
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.
基金Supported by the National Natural Science Foundation of China (No. 61173036)
文摘The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected. Then, a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices. The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and auto-correlation with the natural frequency of the plaintext being hidden and homogenized.
文摘The assumption of static and deterministic conditions is common in the practice of construction project planning. However, at the construction phase, projects are subject to uncertainty. This may lead to serious schedule disruptions and, as a consequence, serious revisions oft.he schedule baseline. The aim of the paper is developing a method for constructing robust project schedules with a proactive procedure. Robust project scheduling allows for constructing stable schedules with time buffers introduced to cope with multiple disruptions during project execution. The method proposed by the authors, based on Monte Carlo simulation technique and mathematical programming for buffer sizing optimization, was applied to scheduling an example project. The results were compared, in terms of schedule stability, to those of the float factor heuristic procedttre.
文摘In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto(GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective,reliable and does not require any restrictive assumptions for nonlinear terms.
基金Supported by the National Natural Science Foundation of China under Grant No.91130013Hunan Provincial Innovation Foundation under Grant No.CX2012B010+1 种基金the Innovation Fund of National University of Defense Technology under Grant No.B120205the Open Foundation of State Key Laboratory
文摘Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
