Overview

The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The delta-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field.

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9789810213480

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"The remarkable discovery for the algebraic structure governing the sequence of conserved quantities in the kdV, KP or non-linear Schr dinger dynamics was a long time restricted to a one-dimensional spatial coordinate system. The multidimensional analogs are much harder and for this reason very intriguing to tame. The book by Konopelchenko offers a first organized exposition of the inverse spectral transform technique applied to 2D integrable systems of the same category. The elegant and original combination of complex analysis, spectral theory and infinite dimensional algebra is a high mark of this text. -- Professor Mihai Putinar ""University of California at Santa Barbara"""

The remarkable discovery for the algebraic structure governing the sequence of conserved quantities in the kdV, KP or non-linear Schr dinger dynamics was a long time restricted to a one-dimensional spatial coordinate system. The multidimensional analogs are much harder and for this reason very intriguing to tame. The book by Konopelchenko offers a first organized exposition of the inverse spectral transform technique applied to 2D integrable systems of the same category. The elegant and original combination of complex analysis, spectral theory and infinite dimensional algebra is a high mark of this text. -- Professor Mihai Putinar University of California at Santa Barbara

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