This article is cited in 17 papers

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

M. Boiti^a, F. Pempinelli^a, A. K. Pogrebkov<sup>b

a</sup> Lecce University
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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.

Language: English

 English version: Theoretical and Mathematical Physics, 1994, 99:2, 511–522

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