| Autor: |
Da-jun Zhang |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Partial Differential Equations in Applied Mathematics, Vol 5, Iss , Pp 100362- (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2666-8181 |
| DOI: |
10.1016/j.padiff.2022.100362 |
| Popis: |
In this paper I give a short review on the continuous, semi-discrete and discrete Burgers equations, which are featured as integrable equations that are linearisable. The review focuses more on connections of these three kinds of equations and connections with (2+1)-dimensional systems. The continuous Burgers hierarchy is a reduction of the derivative nonlinear Schrödinger hierarchy. The later is a result of the squared eigenfunction symmetry constraint of the modified Kadomtsev–Petviashvili system. The semi-discrete Burgers hierarchy can be considered as Bäcklund transformations of the continuous Burgers hierarchy. They are also reductions of the relativistic Toda hierarchy, which is a consequence of the squared eigenfunction symmetry constraint of the semi-discrete modified Kadomtsev–Petviashvili system. The fully discrete Burgers equation is the Bianchi identity of the Bäcklund transformation for the continuous Burgers hierarchy. It is 3-point lattice equation, three-dimensionally consistent, and linearisable. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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