摘要
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.
基金
supported by the National Natural Science Foundation of China(Nos.11201251,10971109)
the Natural Science Foundation of Zhejiang Province(No.LY12A01007)
the K.C.Wong Magna Fundin Ningbo University
