| Autor: |
Wei, Xueli, van der Kamp, Peter H., Zhang, Da-jun |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1088/1572-9494/abfcba |
| Popis: |
An auto-B\"acklund transformation for the quad equation $\mathrm{Q1}_1$ is considered as a discrete equation, called $\mathrm{H2}^a$, which is a so called torqued version of $\mathrm{H2}$. The equations $\mathrm{H2}^a$ and $\mathrm{Q1}_1$ compose a consistent cube, from which a auto-B\"acklund transformation and a Lax pair for $\mathrm{H2}^a$ are obtained. More generally it is shown that auto-B\"acklund transformations admit auto-B\"acklund transformations. Using the auto-B\"acklund transformation for $\mathrm{H2}^a$ we derive a seed solution and a one-soliton solution. From this solution it is seen that $\mathrm{H2}^a$ is a semi-autonomous lattice equation, as the spacing parameter $q$ depends on $m$ but it disappears from the plain wave factor. |
| Databáze: |
arXiv |
| Externí odkaz: |
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