We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end...We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).展开更多
The principles for the modulus method and the percentage method are established and discussed in the part following Part Ⅰ of the series papers, in which we proposed the various algorithms of the strength method and ...The principles for the modulus method and the percentage method are established and discussed in the part following Part Ⅰ of the series papers, in which we proposed the various algorithms of the strength method and the work method. The samples of Wool/PET blended fibre bundles, the method of fibre-bundle tensile tests and the typical specific stress-extension curves from the fibre bundles with different blend ratios are the same as in Part Ⅰ. It can be found that the theoretical results estimated by the modulus and percentage methods accord with the experimental values highly though the calculations of the two methods are slightly more complex than those of the strength and work methods. Especially, using the modulus method can not only avoid the influence of the error caused by the determination of the tensile curve of no fibre breaking in stretching, Y(e), but also need not to know the tensile curves of mono-component fibre bundles in certain calculation. The latter advantage of the modulus method exists in the percentage method too, but it should adopt the improved calculation of ones.展开更多
In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its...In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.展开更多
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).
文摘The principles for the modulus method and the percentage method are established and discussed in the part following Part Ⅰ of the series papers, in which we proposed the various algorithms of the strength method and the work method. The samples of Wool/PET blended fibre bundles, the method of fibre-bundle tensile tests and the typical specific stress-extension curves from the fibre bundles with different blend ratios are the same as in Part Ⅰ. It can be found that the theoretical results estimated by the modulus and percentage methods accord with the experimental values highly though the calculations of the two methods are slightly more complex than those of the strength and work methods. Especially, using the modulus method can not only avoid the influence of the error caused by the determination of the tensile curve of no fibre breaking in stretching, Y(e), but also need not to know the tensile curves of mono-component fibre bundles in certain calculation. The latter advantage of the modulus method exists in the percentage method too, but it should adopt the improved calculation of ones.
基金The project partially supported by National Natural Science Foundation of China
文摘In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.
