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 ⁽⁰’⁰⁾ and ⁽¹’⁰⁾ variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of ⁽⁰’⁰⁾ and ⁽¹’⁰⁾ in terms of their 3-dimensional consistency, Lax pair, bilinear form, and continuum...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | 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 |
| Цитувати: | A Revisit to the ABS H2 Equation. Aye Aye Cho, Maebel Mesfun and Da-Jun Zhang. SIGMA 17 (2021), 093, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862598883844030464 |
|---|---|
| author | Cho, Aye Aye Mesfun, Maebel Zhang, Da-Jun |
| author_facet | Cho, Aye Aye Mesfun, Maebel Zhang, Da-Jun |
| citation_txt | A Revisit to the ABS H2 Equation. Aye Aye Cho, Maebel Mesfun and Da-Jun Zhang. SIGMA 17 (2021), 093, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly related to the ⁽⁰’⁰⁾ and ⁽¹’⁰⁾ variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of ⁽⁰’⁰⁾ and ⁽¹’⁰⁾ in terms of their 3-dimensional consistency, Lax pair, bilinear form, and continuum limits. It is shown that ⁽¹’⁰⁾itself satisfies a 9-point lattice equation, and in the continuum limit ⁽¹’⁰⁾ is related to the eigenfunction in the Lax pair of the Korteweg-de Vries equation.
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| first_indexed | 2026-03-14T00:42:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211434 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T00:42:08Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cho, Aye Aye Mesfun, Maebel Zhang, Da-Jun 2026-01-02T08:32:47Z 2021 A Revisit to the ABS H2 Equation. Aye Aye Cho, Maebel Mesfun and Da-Jun Zhang. SIGMA 17 (2021), 093, 19 pages 1815-0659 2020 Mathematics Subject Classification: 35Q51; 35Q55; 37K60 arXiv:2106.12835 https://nasplib.isofts.kiev.ua/handle/123456789/211434 https://doi.org/10.3842/SIGMA.2021.093 In this paper, we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly related to the ⁽⁰’⁰⁾ and ⁽¹’⁰⁾ variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of ⁽⁰’⁰⁾ and ⁽¹’⁰⁾ in terms of their 3-dimensional consistency, Lax pair, bilinear form, and continuum limits. It is shown that ⁽¹’⁰⁾itself satisfies a 9-point lattice equation, and in the continuum limit ⁽¹’⁰⁾ is related to the eigenfunction in the Lax pair of the Korteweg-de Vries equation. The authors are grateful to the referees for their invaluable comments. This project is supported by the NSF of China (Nos. 11631007 and 11875040) and the Science and Technology Innovation Plan of Shanghai (No. 20590742900). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Revisit to the ABS H2 Equation Article published earlier |
| spellingShingle | A Revisit to the ABS H2 Equation Cho, Aye Aye Mesfun, Maebel Zhang, Da-Jun |
| title | A Revisit to the ABS H2 Equation |
| title_full | A Revisit to the ABS H2 Equation |
| title_fullStr | A Revisit to the ABS H2 Equation |
| title_full_unstemmed | A Revisit to the ABS H2 Equation |
| title_short | A Revisit to the ABS H2 Equation |
| title_sort | revisit to the abs h2 equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211434 |
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