Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+ l)-dimensional cubic nonlinear Schrodinger (NLS) equation and its corresponding cyl...Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+ l)-dimensional cubic nonlinear Schrodinger (NLS) equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.展开更多
Abstract By applying the Lie group method, the (2+l)-dimensional soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional brea...Abstract By applying the Lie group method, the (2+l)-dimensional soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional breaking soliton equation are obtained.展开更多
By means of the generalized direct method,a relationship is constructed between the new solutions andthe old ones of the (3+1)-dimensional breaking soliton equation.Based on the relationship,a new solution is obtained...By means of the generalized direct method,a relationship is constructed between the new solutions andthe old ones of the (3+1)-dimensional breaking soliton equation.Based on the relationship,a new solution is obtainedby using a given solution of the equation.The symmetry is also obtained for the (3+1)-dimensional breaking solitonequation.By using the equivalent vector of the symmetry,we construct a seven-dimensional symmetry algebra and getthe optimal system of group-invariant solutions.To every case of the optimal system,the (3+1)-dimensional breakingsoliton equation is reduced and some solutions to the reduced equations are obtained.Furthermore,some new explicitsolutions are found for the (3+1)-dimensional breaking soliton equation.展开更多
Projections of geodetic are important for all countries all over the world, where using system coordinates for solving any problems in measurements of surveying works. Russell projection is one of projections used in ...Projections of geodetic are important for all countries all over the world, where using system coordinates for solving any problems in measurements of surveying works. Russell projection is one of projections used in some countries. Direct algorithms in this projection use two methods. The first method uses partial differential equation, which is not after six orders in the series. While, the second method uses traditional series (exponential series), which is very difficult and requires complex statistical analysis. New methodology has been applied for direct algorithms in Russell projection using general law of unlimited algorithms by simple method.展开更多
In this paper exact solutions of a new modified nonlinearly dispersive equation (simply called inK(m, n, a, b) Ua Ub equation), u^m-1 ut + α( u^n)x +β(u^a(u^b)xx)x = 0, is investigated by using some dir...In this paper exact solutions of a new modified nonlinearly dispersive equation (simply called inK(m, n, a, b) Ua Ub equation), u^m-1 ut + α( u^n)x +β(u^a(u^b)xx)x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions (solitons with the absence of infinite wings) and solitary pattern solutions (having infinite slopes or cusps) are obtained.展开更多
This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonli...This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser's motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser's vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.展开更多
基金The project supported by K.C. Wong Magna Fund in Ningbo University, National Natural Science Foundation of China under Grant Nos. 10747141 and 10735030;Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408;Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093;National Basic Research Program of China (973 Program 2007CB814800);Program for Changjiang Scholars and Innovative Research Team in University (IRTO734)
文摘Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+ l)-dimensional cubic nonlinear Schrodinger (NLS) equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004zx16
文摘Abstract By applying the Lie group method, the (2+l)-dimensional soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional breaking soliton equation are obtained.
基金National Natural Science Foundation of China under Grant No.10735030Shanghai Leading Academic Discipline Project under Grant No.B412+1 种基金Natural Science Foundations of Zhejiang Province of China under Grant No.Y604056the Doctoral Foundation of Ningbo City under Grant No.2005A61030
文摘By means of the generalized direct method,a relationship is constructed between the new solutions andthe old ones of the (3+1)-dimensional breaking soliton equation.Based on the relationship,a new solution is obtainedby using a given solution of the equation.The symmetry is also obtained for the (3+1)-dimensional breaking solitonequation.By using the equivalent vector of the symmetry,we construct a seven-dimensional symmetry algebra and getthe optimal system of group-invariant solutions.To every case of the optimal system,the (3+1)-dimensional breakingsoliton equation is reduced and some solutions to the reduced equations are obtained.Furthermore,some new explicitsolutions are found for the (3+1)-dimensional breaking soliton equation.
文摘Projections of geodetic are important for all countries all over the world, where using system coordinates for solving any problems in measurements of surveying works. Russell projection is one of projections used in some countries. Direct algorithms in this projection use two methods. The first method uses partial differential equation, which is not after six orders in the series. While, the second method uses traditional series (exponential series), which is very difficult and requires complex statistical analysis. New methodology has been applied for direct algorithms in Russell projection using general law of unlimited algorithms by simple method.
基金Sponsored by K.C.Wong Magna Fund in Ningbo University and Ningbo Natural Science Foundation under Grant Nos.2008A610017 and 2007A610049
文摘In this paper exact solutions of a new modified nonlinearly dispersive equation (simply called inK(m, n, a, b) Ua Ub equation), u^m-1 ut + α( u^n)x +β(u^a(u^b)xx)x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions (solitons with the absence of infinite wings) and solitary pattern solutions (having infinite slopes or cusps) are obtained.
文摘This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser's motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser's vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.