Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of ...Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.展开更多
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
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10371098 and the Natural Science Foundation of Shaanxi Province of ChinaIt is my pleasure to thank Prof. Qu Chang-Zheng for his helpful discussion
文摘Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.
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).
