A thesis accepted by Tallinn Technical University for the Degree of Doctor of Philosophy in Natural Sciences
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Abstract:  The aim of this thesis is to find a detailed description of multisoliton interactions. For that multisoliton solutions of KdV type equations are defined, constructed, and analyzed in phase variables. As a result of the analysis, the concept of an interaction soliton is introduced and a novel decomposition of multisoliton solutions is proposed. According to the decomposition, a multisoliton solution is a linear superposition of solitons and interaction solitons. The concept of the interaction soliton is exploited to interpret multisoliton interactions. A geometric representation of interaction patterns is introduced and an algorithmic way to construct the interaction patterns for an arbitrary number of solitons is proposed and implemented. All new concepts are illustrated for twosoliton interactions, examples are given also for three and fivesoliton interactions. For exemplifying models of soliton interactions, the KdV, KdVSawadaKotera, and KP equations are used. As a practical application of these findings, an inverse problem of wave crests is introduced. The uniqueness of a solution to the inverse problem is proved for the KP twosoliton interactions. Sensitivity of this solution is analyzed against possible measurement errors. 
Place/venue:  The presentation of the thesis took place on November 7th, 2001, at Institute of Cybernetics at TTU, Tallinn, Estonia. 
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Booklet:  ISSN 14064723, ISBN 9985592336 
Copyright:  Pearu Peterson, 2001 
Releated talks:  P. Peterson and E. van Groesen. Wave interaction patterns and prediction of wave parameters. In Symposium on Mathematical Support for Hydrodynamic Laboratories (LabMath), Institut Teknologi Bandung, Indonesia, September 911, 2001. P. Peterson and E. van Groesen. The direct and inverse problem of wave crests. In 20th International Congress of Theoretical and Applied Mechanics  ICTAM 2000, Chicago, USA, August 27September 2, 2000 