Article Dans Une Revue Journal of Mathematical Physics Année : 2022

ON (t 2 , t 3 )−ZAKHAROV-SHABAT EQUATIONS OF GENERALIZED KADOMTSEV-PETVIASHVILI HIERARCHIES

Enrique Reyes
Vladimir Rubtsov
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Résumé

We review the integration of the KP hierarchy in several nonstandard 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; a Moyal algebra. In all these cases we can formulate and solve the Cauchy problem of the KP hierarchy. Also, in each of these cases we derive different Zakharov-Shabat (t 2 , t 3)-equations-that is, different Kadomtsev-Petviashvili equations-and we prove existence of solutions arising from solutions to the corresponding KP hierarchy.

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hal-03606717 , version 1 (12-03-2022)

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Jean-Pierre Magnot, Enrique Reyes, Vladimir Rubtsov. ON (t 2 , t 3 )−ZAKHAROV-SHABAT EQUATIONS OF GENERALIZED KADOMTSEV-PETVIASHVILI HIERARCHIES. Journal of Mathematical Physics, 2022, 63, pp.093501. ⟨10.1063/5.0093238⟩. ⟨hal-03606717⟩
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