ON THE KADOMTSEV-PETVIASHVILI HIERARCHY IN AN EXTENDED CLASS OF FORMAL PSEUDO-DIFFERENTIAL OPERATORS - Archive ouverte HAL Access content directly
Journal Articles Theoretical and Mathematical Physics Year : 2021

ON THE KADOMTSEV-PETVIASHVILI HIERARCHY IN AN EXTENDED CLASS OF FORMAL PSEUDO-DIFFERENTIAL OPERATORS

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Abstract

We study the existence and uniqueness of the Kadomtsev-Petviashvili (KP) hierarchy solutions in the algebra of F Cl(S 1 , K n) of formal classical pseudo-differential operators. The classical algebra ΨDO(S 1 , K n) where the KP hierarchy is well-known appears as a subalgebra of F Cl(S 1 , K n). We investigate algebraic properties of F Cl(S 1 , K n) such as splittings, r-matrices, extension of the Gelfand-Dickii bracket, almost complex structures. Then, we prove the existence and uniqueness of the KP hierarchy solutions in F Cl(S 1 , K n) with respect to extended classes of initial values. Finally, we extend this KP hierarchy to complex order formal pseudo-differential operators and we describe their Hamiltonian structures similarly to previously known formal case. .
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Dates and versions

hal-03104685 , version 1 (09-01-2021)

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  • HAL Id : hal-03104685 , version 1

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Jean-Pierre Magnot, Vladimir Roubtsov. ON THE KADOMTSEV-PETVIASHVILI HIERARCHY IN AN EXTENDED CLASS OF FORMAL PSEUDO-DIFFERENTIAL OPERATORS. Theoretical and Mathematical Physics , In press. ⟨hal-03104685⟩
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