Kadomtsev–petviashvili hierarchy: Negative times

Andrei K. Pogrebkov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number1988
Issue number16
Publication statusPublished - 2 Aug 2021
Externally publishedYes


  • Commutator identities
  • Integrable hierarchies
  • Reductions


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