Displacement memory for flyby

Zel'dovich and Polnarev, in their seminal paper [1] suggested that a gravitational wave generated by flyby would merely displace the particles. We confirm their prediction numerically by fine-tuning the wave profile proposed by Gibbons and Hawking [2], and then analytically for its approximation by a P\"oschl-Teller potential. Higher-order derivative profiles proposed for gravitational collapse, etc [2] are shortly discussed.
Comment: Revised and extended version which includes also J. Balog as co-author. 28 pages, many figures. accepted for publication in Annals of Physics