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Media type:
Electronic Thesis;
Doctoral Thesis;
E-Book;
Text
Title:
The Dressing method: Application to selected integrable models
Contributor:
Gruner, Kevin Tim
[Author]
imprint:
Cologne University: KUPS, 2021-03-19
Language:
German;
English
Origination:
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
The AKNS system, an integrable system of partial differential equations (PDEs), has been introduced in 1974 by and named after Mark J. Ablowitz, David J. Kaup, Alan C. Newell and Harvey Segur. Following the scheme developed for these systems, the integrable initial value problem on the line can be rewritten as a compatibility condition, or as a zero curvature condition, of two linear ordinary differential equations. Important examples falling into this category are the nonlinear Schrödinger (NLS) equation and the sine-Gordon (sG) equation. A particular class of internal boundary conditions, the defect conditions, have been investigated for which in some cases it can be verified that integrability is preserved. Further, the combination of such a defect condition with a boundary condition has in specific cases proven instructive in the derivation of integrable initial-boundary value problems regarding the mentioned PDEs on the half-line. Particularly, the new boundary conditions for the NLS equation on the half-line have been constructed through this approach. However, even though integrability of these models has been treated by several authors in the field, the construction of actual solutions is a subject which has been barely worked on. One approach in the direction of solution construction has been developed based on the ideas of the unified transform method combined with the Dressing method, which is commonly known as dressing the boundary. In this thesis, we develop this method further and apply it to all models mentioned thereby constructing explicit soliton solutions therein.