It is shown that the Affine Toda models (AT) constitute a ``gauge fixed''version of the Conformal Affine Toda model (CAT). This result enables one tomap every solution of the AT models into an infinite number of solutions of thecorresponding CAT models, each one associated to a point of the orbit of theconformal group. The Hirota's $\tau$-function are introduced and solitonsolutions for the AT and CAT models associated to $\hat {SL}(r+1)$ and $\hat{SP}(r)$ are constructed.
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机译：结果表明，仿射Toda模型（AT）构成了保形仿射Toda模型（CAT）的``量规固定''版本。这一结果使人们可以将AT模型的每个解映射到相应CAT模型的无数解中，每个解与保形群轨道的一个点相关联。介绍了Hirota的$ \ tau $函数，并构造了与$ \ hat {SL}（r + 1）$和$ \ hat {SP}（r）$相关的AT和CAT模型的孤子解。
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