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| Loop Algebras and Bi-integrable Couplings |
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Citation： |
Wenxiu MA.Loop Algebras and Bi-integrable Couplings[J].Chinese Annals of Mathematics B,2012,33(2):207~224 |
| Page view： 1872
Net amount： 1652 |
Authors： |
Wenxiu MA; |
Foundation： |
the State Administration of Foreign Experts Affairs of China, the National Natural Science Foundation of China (Nos. 10971136, 10831003, 61072147, 11071159), the Chunhui Plan of the Ministry of Education of China, the Innovation Project of Zhejiang Province (No. T200905), the 1Natural Science Foundation of Shanghai (No. 09ZR1410800) and the Shanghai Leading Academic Discipline Project (No. J50101). |
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| Abstract： |
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations. The variational identities under non-degenerate, symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy. |
Keywords： |
Loop algebra,Bi-integrable coupling, Zero curvature equation, Symmetry, Hamiltonian structure |
Classification： |
37K05, 37K10, 35Q58 |
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