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

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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https://hal.archives-ouvertes.fr/hal-03104685
Contributor : Jean-Pierre Magnot Connect in order to contact the contributor
Submitted on : Saturday, January 9, 2021 - 4:42:34 PM
Last modification on : Wednesday, October 20, 2021 - 3:19:02 AM
Long-term archiving on: : Saturday, April 10, 2021 - 6:15:54 PM

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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 , Springer, In press. ⟨hal-03104685⟩

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