A modified direct optimization method is proposed to solve the optimal multi-revolution transfer with low-thrust between Earth-orbits. First, through parameterizing the control steering angles by costate variables, th...A modified direct optimization method is proposed to solve the optimal multi-revolution transfer with low-thrust between Earth-orbits. First, through parameterizing the control steering angles by costate variables, the search space of free parameters has been decreased. Then, in order to obtain the global optimal solution effectively and robustly, the simulated annealing and penalty function strategies were used to handle the constraints, and a GA/SQP hybrid optimization algorithm was utilized to solve the parameter optimization problem, in which, a feasible suboptimal solution obtained by GA was submitted as an initial parameter set to SQP for refinement. Comparing to the classical direct method, this novel method has fewer free parameters, needs not initial guesses, and has higher computation precision. An optimal-fuel transfer problem from LEO to GEO was taken as an example to validate the proposed approach. The results of simulation indicate that our approach is available to solve the problem of optimal muhi-revolution transfer between Earth-orbits.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 we are concerned with the modified conjugate direction method for computing the pseudoinverse by using an orthogonal basis of the range space of A. Numerical results show that the new method retains some...In this paper we are concerned with the modified conjugate direction method for computing the pseudoinverse by using an orthogonal basis of the range space of A. Numerical results show that the new method retains some main advantages in terms of efficiency and accuracy.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
In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, ...In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.展开更多
In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）-...Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.展开更多
This paper analyses and compares the property of the Modified Bayesian Directional spectrum analysis Method （MBDM） and the Modified Maximum Lkelihood Method （MMLM） that can he used to estimate directional spectrum...This paper analyses and compares the property of the Modified Bayesian Directional spectrum analysis Method （MBDM） and the Modified Maximum Lkelihood Method （MMLM） that can he used to estimate directional spectrum and reflected coefficient of phase-locked wave field overlapped by multi directional irregular incident and reflected waves. The numerical test verifies the results under different wave conditions, different measurement systems, and different reflection features. The computation speed and stability of the two methods is also compared. The analysis addresses that the MBDM is better than the MMLM for directional spectrum estimating, while the MMLM is better than the MBDM for reflected coefficient estimation and calculating speed and stability.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.10672044)
文摘A modified direct optimization method is proposed to solve the optimal multi-revolution transfer with low-thrust between Earth-orbits. First, through parameterizing the control steering angles by costate variables, the search space of free parameters has been decreased. Then, in order to obtain the global optimal solution effectively and robustly, the simulated annealing and penalty function strategies were used to handle the constraints, and a GA/SQP hybrid optimization algorithm was utilized to solve the parameter optimization problem, in which, a feasible suboptimal solution obtained by GA was submitted as an initial parameter set to SQP for refinement. Comparing to the classical direct method, this novel method has fewer free parameters, needs not initial guesses, and has higher computation precision. An optimal-fuel transfer problem from LEO to GEO was taken as an example to validate the proposed approach. The results of simulation indicate that our approach is available to solve the problem of optimal muhi-revolution transfer between Earth-orbits.
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.
文摘In this paper we are concerned with the modified conjugate direction method for computing the pseudoinverse by using an orthogonal basis of the range space of A. Numerical results show that the new method retains some main advantages in terms of efficiency and accuracy.
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Project supported by the National Natural Science Foundation of China (Grant No. 11175092)the Scientific Research Fund of Education Department of Zhejiang Province of China (Grant No. Y201017148)K. C. Wong Magna Fund in Ningbo University
文摘In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金supported by the Natural Science Foundation of Shandong Province of China under Grant Nos.Q2005A01
文摘Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.
文摘This paper analyses and compares the property of the Modified Bayesian Directional spectrum analysis Method （MBDM） and the Modified Maximum Lkelihood Method （MMLM） that can he used to estimate directional spectrum and reflected coefficient of phase-locked wave field overlapped by multi directional irregular incident and reflected waves. The numerical test verifies the results under different wave conditions, different measurement systems, and different reflection features. The computation speed and stability of the two methods is also compared. The analysis addresses that the MBDM is better than the MMLM for directional spectrum estimating, while the MMLM is better than the MBDM for reflected coefficient estimation and calculating speed and stability.
