Some new methods and results in the theory of (2+1)-dimensional integrable equations

M. Boiti, F. Pempinelli, A. K. Pogrebkov

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


The general resolvent scheme for solving nonlinear integrable evolution equations is formulated. Special attention is paid to the problem of nontrivial dressing and the corresponding transformation of spectral data. The 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 the corresponding Jost solutions and spectral data with given initial data u(0, x, y) belonging to the Schwartz space are presented.

Original languageEnglish
Pages (from-to)511-522
Number of pages12
JournalTheoretical and Mathematical Physics
Issue number2
Publication statusPublished - May 1994
Externally publishedYes


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