A Revisit to the ABS H2 Equation
In this paper, we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly related to the 𝑆⁽⁰’⁰⁾ and 𝑆⁽¹’⁰⁾ variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of 𝑆⁽⁰’⁰⁾ and 𝑆⁽¹’⁰⁾ in terms of their 3-dimensional consistency, Lax pair, bilinear form, and conti...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211434 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Revisit to the ABS H2 Equation. Aye Aye Cho, Maebel Mesfun and Da-Jun Zhang. SIGMA 17 (2021), 093, 19 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | In this paper, we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly related to the 𝑆⁽⁰’⁰⁾ and 𝑆⁽¹’⁰⁾ variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of 𝑆⁽⁰’⁰⁾ and 𝑆⁽¹’⁰⁾ in terms of their 3-dimensional consistency, Lax pair, bilinear form, and continuum limits. It is shown that 𝑆⁽¹’⁰⁾itself satisfies a 9-point lattice equation, and in the continuum limit 𝑆⁽¹’⁰⁾ is related to the eigenfunction in the Lax pair of the Korteweg-de Vries equation.
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| ISSN: | 1815-0659 |