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arXiv · 2607.21052

Gauge-Theoretical Method in Solving Zero-curvature Equations III --Gauge Theoretical Method and the B\"acklund Transformations for Solitons--

Takahiro Azuma·Takao Koikawa
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Abstract

In soliton theory, both the gauge-theoretical method and the B\"acklund 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 B\"acklund 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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Takahiro Azuma, Takao Koikawa. 2026-07-23. Gauge-Theoretical Method in Solving Zero-curvature Equations III --Gauge Theoretical Method and the B\"acklund Transformations for Solitons--. https://arxiv.org/abs/2607.21052

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