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A Kind of Discretization of the KdV Hierarchy
R. L. Linab a CEA, Service de Physique Théorique
b Tsinghua University
Abstract:
We propose a method for introducing higher-order terms in the potential expansion in order to study the continuum limits of the Toda hierarchy. These higher-order terms are differential polynomials in the lower-order terms. This type of potential expansion allows using fewer equations in the Toda hierarchy to recover the KdV hierarchy by the so-called recombination method. We show that the Lax pairs, the Poisson tensors, and the Hamiltonians of the Toda hierarchy tend toward the corresponding objects of the KdV hierarchy in the continuum limit. This method gives a kind of discretization of the KdV hierarchy.
Keywords:
continuum limit, Toda hierarchy, KdV hierarchy.
Citation:
R. L. Lin, “A Kind of Discretization of the KdV Hierarchy”, TMF, 137:2 (2003), 209–219; Theoret. and Math. Phys., 137:2 (2003), 1534–1543
Linking options:
https://www.mathnet.ru/eng/tmf266https://doi.org/10.4213/tmf266 https://www.mathnet.ru/eng/tmf/v137/i2/p209
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Abstract page: | 256 | Full-text PDF : | 156 | References: | 27 | First page: | 1 |
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