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The Recursion Operator of the Kadomtsev‐Petviashvili Equation and the Squared Eigenfunctions of the Schrödinger Operator
Author(s) -
Fokas A. S.,
Santini P. M.
Publication year - 1986
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1986752179
Subject(s) - eigenfunction , mathematics , operator (biology) , kadomtsev–petviashvili equation , recursion (computer science) , ladder operator , mathematical analysis , hamiltonian (control theory) , shift operator , finite rank operator , momentum operator , multiplication operator , mathematical physics , semi elliptic operator , compact operator , partial differential equation , eigenvalues and eigenvectors , physics , burgers' equation , differential operator , quantum mechanics , algorithm , computer science , repressor , banach space , chemistry , mathematical optimization , biochemistry , hilbert space , transcription factor , programming language , extension (predicate logic) , gene
The recursion operator of the Kadomtsev‐Petviashvili equation is algorithmically derived. This recursion operator is the two‐spatial‐dimensional analogue of the Lenard operator of the Korteweg‐deVries equation. It is also the “squared” eigenfunction operator of the time‐dependent Schrödinger operator. The existence of the recursion operator suggests that the Kadomtsev‐Petviashvili equation is a hi‐Hamiltonian system.