### Abstract

The conserved quantities and symmetries of the soliton equations included in the 2DTL (two-dimensional Toda lattice) hierarchy are considered by means of the theory of the τ function. A typical example is presented for the 2DTL equation that is the simplest nontrivial equation in the hierarchy. Then, by applying suitable reductions, the cases of the Toda lattice equation and the sine-Gordon equation are discussed.

Original language | English |
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Pages (from-to) | 506-514 |

Number of pages | 9 |

Journal | Journal of Mathematical Physics |

Volume | 32 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1991 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Kajiwara, K., & Satsuma, J. (1991). The conserved quantities and symmetries of the two-dimensional Toda lattice hierarchy.

*Journal of Mathematical Physics*,*32*(2), 506-514. https://doi.org/10.1063/1.529387