AI 中文总结
研究孤子理论中规范理论方法与巴克伦德变换的异同，通过将巴克伦德变换限制在不同孤子数的解上获得见解，并用实例展示如何构造不同孤子数的孤子解。
AI 中文摘要
在孤子理论中，规范理论方法和巴克伦德变换都从一对线性方程的相容性条件得出孤子方程。因此，有必要厘清这两种方法的异同。巴克伦德变换定义了从一个孤子解到另一个孤子解的变换。特别地，将变换限制在具有不同孤子数的解上能得到有趣的见解。我们通过几个例子展示了如何构造具有不同孤子数的孤子解。
英文摘要
In soliton theory, both the gauge-theoretical method and the Bäcklund transformation yield soliton equations from the compatibility condition of a pair of linear equations. Therefore, it is necessary to clarify the similarities and differences between these two methods. The Bäcklund transformation defines a transformation from one soliton solution to another. In particular, restricting the transformation to solutions with different soliton numbers yields interesting insights. Using several examples, we demonstrate how soliton solutions with different soliton numbers are constructed.
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