# Bi-infinite Solutions for KdV- and Toda-Type Discrete Integrable Systems Based on Path Encodings

@article{Croydon2020BiinfiniteSF, title={Bi-infinite Solutions for KdV- and Toda-Type Discrete Integrable Systems Based on Path Encodings}, author={David A. Croydon and Makiko Sasada and Satoshi Tsujimoto}, journal={Mathematical Physics, Analysis and Geometry}, year={2020}, volume={25} }

We define bi-infinite versions of four well-studied discrete integrable models, namely the ultra-discrete KdV equation, the discrete KdV equation, the ultra-discrete Toda equation, and the discrete Toda equation. For each equation, we show that there exists a unique solution to the initial value problem when the given data lies within a certain class, which includes the support of many shift ergodic measures. Our unified approach, which is also applicable to other integrable systems defined…

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