Volume 15, Issue 1, March 2008, Pages 48 - 65
On the (2+1)-Dimensional Extension of 1-Dimensional Toda Lattice Hierarchy
Received 23 May 2007, Accepted 5 November 2007, Available Online 1 March 2008.
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- We introduce a (2+1)-dimensional extension of the 1-dimensional Toda lattice hierar- chy. The hierarchy is given by two different formulations. For the first formulation, we obtain the bilinear identity for the ? -functions and construct explicit solutions ex- pressed by Wronski determinants. For the second formulation, we obtain the slightly different bilinear identity and clarify the relation to the hierarchy arising from the ho- mogeneous vertex representation of the 2-toroidal Lie algebra sl tor 2 , obtained by Kakei et al.
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Cite this article
TY - JOUR AU - Yuji OGAWA PY - 2008 DA - 2008/03 TI - On the (2+1)-Dimensional Extension of 1-Dimensional Toda Lattice Hierarchy JO - Journal of Nonlinear Mathematical Physics SP - 48 EP - 65 VL - 15 IS - 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2008.15.1.5 DO - https://doi.org/10.2991/jnmp.2008.15.1.5 ID - OGAWA2008 ER -