The scattering transform for the Kadomtsev–Petviashvili equation (KPII) is a local symplectomorphism. Pulling back the Hamiltonians for the linear evolutions of scattering data gives Hamiltonians for the KPII hierarchy: they are values of the associated scattering data at distinguished points. This method yields simple proofs that KPII has infinitely many commuting flows and simplifies their calculation. It also provides a Plancherel‐type theorem.
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© 1988 American Institute of Physics.
1988
American Institute of Physics
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