Darboux transformation method is used for constructing harmonic maps from R2 to U(N).The explicit expressions for Darboux matrices are used to obtain new harmonic maps from aknown one.The algorithm is purely algebraic...Darboux transformation method is used for constructing harmonic maps from R2 to U(N).The explicit expressions for Darboux matrices are used to obtain new harmonic maps from aknown one.The algorithm is purely algebraic and can be repeated successively to obtain aninfinite sequence of harmonic maps. Single and multiple solitons are obtained with geometriccharacterizations and it is proved that the interaction between solitons is elastic. By introducingthe singlllar Darboux transformations, an explicit method to construct new unitons is presented.展开更多
The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a p...The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.展开更多
文摘Darboux transformation method is used for constructing harmonic maps from R2 to U(N).The explicit expressions for Darboux matrices are used to obtain new harmonic maps from aknown one.The algorithm is purely algebraic and can be repeated successively to obtain aninfinite sequence of harmonic maps. Single and multiple solitons are obtained with geometriccharacterizations and it is proved that the interaction between solitons is elastic. By introducingthe singlllar Darboux transformations, an explicit method to construct new unitons is presented.
基金Project supported by the National Natural Science Foundation of China (No.10271106)the Education Commission of Zhejiang Province of China (No.20030342).
文摘The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.
