A Remark on the Hankel Determinant Formula for Solutions of the Toda Equation
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- Kajiwara, Kenji
- Graduate School of Mathematics, Kyushu University
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- Mazzocco, Marta
- School of Mathematics, The University of Manchester
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- Ohta, Yasuhiro
- Department of Mathematics, Kobe University
Abstract
We consider the Hankel determinant formula of the $ \tau $ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $ \tau $ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painleve II and IV equations are recovered. The case of finite lattice is also discussed.
Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality
Journal
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- Journal of Physics A : Mathematical and Theoretical
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Journal of Physics A : Mathematical and Theoretical 40 (42), 12661-12675, 2007-10-19
Faculty of Mathematics, Kyushu University