Regular Solution and Lattice Miura Transformation of Bigraded Toda Hierarchy |
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Authors: | Chuanzhong LI and Jingsong HE |
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Affiliation: | 1. Department of Mathematics, Ningbo University, Ningbo, 315211, Zhejiang, China
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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. |
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Keywords: | Regular solution Lattice Miura transformation Bigraded Toda hierarchy Moment polytope Volterra lattice |
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