Explicit solutions of boundary-value problems for (2 + 1)-dimensional integrable systems |
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Authors: | V L Vereshchagin |
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Institution: | 19804. Institute of Mathematics and Computer Center, Ural Science Center, Russian Academy of Sciences, Ufa, Russia
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Abstract: | Two nonlinear integrable models with two space variables and one time variable, the Kadomtsev-Petviashvili equation and the two-dimensional Toda chain, are studied as well-posed boundary-value problems that can be solved by the inverse scattering method. It is shown that there exists a multitude of integrable boundary-value problems and, for these problems, various curves can be chosen as boundary contours; besides, the problems in question become problems with moving boundaries. A method for deriving explicit solutions of integrable boundary-value problems is described and its efficiency is illustrated by several examples. This allows us to interpret the integrability phenomenon of the boundary condition in the traditional sense, namely as a condition for the availability of wide classes of solutions that can be written in terms of well-known functions. |
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