Geodesic
Some new methods and results in the theory of ($2+1$)-dimensional integrable equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 185-200 
M. Boiti; F. Pempinelli; A. K. Pogrebkov. Some new methods and results in the theory of ($2+1$)-dimensional integrable equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 185-200. http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The general resolvent scheme for solving nonlinear integrable evolution equations is formulated. Special attention is paid for the problem of nontrivial dressing and corresponding transformation of spectral data. Kadomtsev–Petviashvili equation is considered as the standard example of integrable models in $2+1$ dimensions. Properties of the solution $u(t,x,y)$ of the Kadomtsev–Petviashvili I equation as well as corresponding Jost solutions and spectral data with given initial data $u(0,x,y)$ belonging to the Schwartz space are presented.

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