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| Regular Solution and Lattice Miura Transformation of Bigraded Toda Hierarchy |
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Citation： |
Chuanzhong LI,Jingsong HE.Regular Solution and Lattice Miura Transformation of Bigraded Toda Hierarchy[J].Chinese Annals of Mathematics B,2013,34(6):865~884 |
| Page view： 1764
Net amount： 1378 |
Authors： |
Chuanzhong LI; Jingsong HE; |
Foundation： |
National Natural Science Foundation of China (Nos. 11201251, 10971109), theNatural Science Foundation of Zhejiang Province (No. LY12A01007) and the K. C. Wong Magna Fundin Ningbo University |
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| Abstract： |
The authors give finite dimensional exponential solutions of the bigraded Toda
hierarchy (BTH). As a specific example of exponential solutions of the BTH, the authors
consider a regular solution for the (1, 2)-BTH with a 3 × 3-sized Lax matrix, and discuss
some geometric structures of the solution from which the difference between the (1, 2)-
BTH and the original Toda hierarchy is shown. After this, the authors construct another
kind of Lax representation of (N, 1)-BTH which does not use the fractional operator of
Lax operator. Then the authors introduce the lattice Miura transformation of (N, 1)-BTH
which leads to equations depending on one field, and meanwhile some specific examples
which contain the Volterra lattice equation (a useful ecological competition model) are
given. |
Keywords： |
Regular solution, Lattice Miura transformation, Bigraded Toda hierarchy,
Moment polytope, Volterra lattice |
Classification： |
37K05, 37K10, 37K20 |
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