Kadomtsev–Petviashvili Hierarchy: Negative Times
The Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times. The derivation of such systems, as well as the corres...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1988 |
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| author | Andrei K. Pogrebkov |
| author_facet | Andrei K. Pogrebkov |
| author_sort | Andrei K. Pogrebkov |
| collection | DOAJ |
| description | The Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times. The derivation of such systems, as well as the corresponding hierarchy, is based on the commutator identities. This approach enables introduction of linear differential equations that admit lifts up to nonlinear integrable ones by means of the special dressing procedure. Thus, one can construct not only nonlinear equations, but corresponding Lax pairs as well. The Lax operator of this evolution coincides with the Lax operator of the “positive” hierarchy. We also derive (1 + 1)-dimensional reductions of equations of this hierarchy. |
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| format | Article |
| id | doaj.art-6c946c2b567e4a9698353e1ab46019d8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:05Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6c946c2b567e4a9698353e1ab46019d82023-11-22T08:34:53ZengMDPI AGMathematics2227-73902021-08-01916198810.3390/math9161988Kadomtsev–Petviashvili Hierarchy: Negative TimesAndrei K. Pogrebkov0Steklov Mathematical Institute, Russian Academy of Sciences, 119991 Moscow, RussiaThe Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times. The derivation of such systems, as well as the corresponding hierarchy, is based on the commutator identities. This approach enables introduction of linear differential equations that admit lifts up to nonlinear integrable ones by means of the special dressing procedure. Thus, one can construct not only nonlinear equations, but corresponding Lax pairs as well. The Lax operator of this evolution coincides with the Lax operator of the “positive” hierarchy. We also derive (1 + 1)-dimensional reductions of equations of this hierarchy.https://www.mdpi.com/2227-7390/9/16/1988commutator identitiesintegrable hierarchiesreductions |
| spellingShingle | Andrei K. Pogrebkov Kadomtsev–Petviashvili Hierarchy: Negative Times Mathematics commutator identities integrable hierarchies reductions |
| title | Kadomtsev–Petviashvili Hierarchy: Negative Times |
| title_full | Kadomtsev–Petviashvili Hierarchy: Negative Times |
| title_fullStr | Kadomtsev–Petviashvili Hierarchy: Negative Times |
| title_full_unstemmed | Kadomtsev–Petviashvili Hierarchy: Negative Times |
| title_short | Kadomtsev–Petviashvili Hierarchy: Negative Times |
| title_sort | kadomtsev petviashvili hierarchy negative times |
| topic | commutator identities integrable hierarchies reductions |
| url | https://www.mdpi.com/2227-7390/9/16/1988 |
| work_keys_str_mv | AT andreikpogrebkov kadomtsevpetviashvilihierarchynegativetimes |