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On (t2, t3)-Zakharov–Shabat equations of generalized Kadomtsev–Petviashvili hierarchies.
- Source :
- Journal of Mathematical Physics; 9/1/2022, Vol. 63 Issue 9, p1-11, 11p
- Publication Year :
- 2022
-
Abstract
- We review the integration of the Kadomtsev–Petviashvili (KP) hierarchy in several non-standard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped with a nilpotent derivation, an algebra of functions equipped with a derivation that generalizes the gradient operator, an algebra of quaternion-valued functions, a differential Lie algebra, an algebra of polynomials equipped with the Pincherle differential, and a Moyal algebra. In all these cases, we can formulate and solve the Cauchy problem of the KP hierarchy. In addition, in each of these cases, we derive different Zakharov–Shabat (t<subscript>2</subscript>, t<subscript>3</subscript>)-equations—that is, different Kadomtsev–Petviashvili equations—and we prove the existence of solutions arising from solutions to the corresponding KP hierarchy. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 63
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 159444654
- Full Text :
- https://doi.org/10.1063/5.0093238