PSEUDO: applications of streams and lazy evaluation to integrable models

Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy

“…where U = ϕ 1 , V = ϕ 2 , W = ϕ 3 and X = ϕ 4 . This was calculated using Maple and PSEUDO [18]. Note that although X and Y appear in this Lagrangian, their presence is trivial in that they do not contribute to or feature in the resulting Euler-Lagrange equations.…”

“…In order to avoid notational confusion over the use of subscripts, we let U = ϕ 1 , V = ϕ 2 , W = ϕ 3 and X = ϕ 4 . The following Lagrangians were found using Maple and PSEUDO [18]. In order to obtain L (234) , a Maple procedure based on (1.18) was used.…”

Integrability of a nonlinear evolution equation derived from isoperimetric plane curve motion

“…to determine the Lagrange multiplier field λ in (21) and to find out that the system has no further constraints.…”

“…with all others vanishing, we require the primary constraint to be stationary under time evolution, {Φ(θ), H T } = 0 , to determine the Lagrange multiplier field λ in (21) and to find out that the system has no further constraints.…”

The short pulse hierarchy

“…In these works we have as a main characteristic a hierarchy of integrable equations with positive and negative flows. Also, throughout this paper the calculations involving pseudo-differential operators were performed or checked by the computer algebra program PSEUDO [9].…”