A thesis accepted by Tallinn Technical University for the Degree of Doctor of Philosophy in Natural Sciences
Author: |
|
---|---|
Promoters: |
|
Opponents: |
|
Abstract: | The aim of this thesis is to find a detailed description of multi-soliton interactions. For that multi-soliton 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 multi-soliton solutions is proposed. According to the decomposition, a multi-soliton solution is a linear superposition of solitons and interaction solitons. The concept of the interaction soliton is exploited to interpret multi-soliton 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 two-soliton interactions, examples are given also for three- and five-soliton interactions. For exemplifying models of soliton interactions, the KdV, KdV-Sawada-Kotera, 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 two-soliton 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. |
Slides: | |
Softcopy: |
|
Booklet: | ISSN 1406-4723, ISBN 9985-59-233-6 |
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 9--11, 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 27--September 2, 2000 |