Constants and pseudo-constants of the Kadomtsev-Petviashvili equation

Abstract

Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n ≥ 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional J _n ⁽ⁿ⁺²⁾ = -1/18 [unk] y ⁿ⁺² q by taking repeated Poisson brackets with the Hamiltonian.

• real and pseudo-constants
• Casimir invariants