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- W3183700164 abstract "The direct linearisation framework is presented for the two-dimensional Toda equations associated with the infinite-dimensional Lie algebras $A_infty$, $B_infty$ and $C_infty$, as well as the Kac--Moody algebras $A_{r}^{(1)}$, $A_{2r}^{(2)}$, $C_{r}^{(1)}$ and $D_{r+1}^{(2)}$ for arbitrary integers $rinmathbb{Z}^+$, from the aspect of a set of linear integral equations in a certain form. Such a scheme not only provides a unified perspective to understand the underlying integrability structure, but also induces the direct linearising type solution potentially leading to the universal solution space, for each class of the two-dimensional Toda system. As particular applications of this framework to the two-dimensional Toda lattices, we rediscover the Lax pairs and the adjoint Lax pairs and simultaneously construct the generalised Cauchy matrix solutions." @default.
- W3183700164 created "2021-08-02" @default.
- W3183700164 creator A5021855408 @default.
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- W3183700164 date "2021-07-24" @default.
- W3183700164 modified "2023-10-16" @default.
- W3183700164 title "Linear integral equations and two‐dimensional Toda systems" @default.
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- W3183700164 doi "https://doi.org/10.1111/sapm.12427" @default.
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