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Matrix Schrödinger equations and Darboux transformations
This thesis contains the matrix generalisations of some important results known in the theory of the scalar Schrödinger operators. In the first part we discuss the onedimensional matrix Schrodinger equations in complex domain. The main results here are the local criteria for the Schrödinger operato...
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1999

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Online Access:  https://hdl.handle.net/2134/28007 
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author  V.M. Goncharenko 
author_facet  V.M. Goncharenko 
author_sort  V.M. Goncharenko (7158659) 
collection  Figshare 
description  This thesis contains the matrix generalisations of some important results known in the theory of the scalar Schrödinger operators. In the first part we discuss the onedimensional matrix Schrodinger equations in complex domain. The main results here are the local criteria for the Schrödinger operators to have trivial monodromy and a matrix generalisation of the wellknown DuistermaatGrünbaum theorem giving the description of such operators in terms of Darboux transformations. In the second part we consider Dintegrable matrix Schrodinger operators in many dimensions. The local criteria on singularities of such operators are found and new examples are constructed. In the last chapter we discuss the soliton solutions of the matrix KdV equations and study the interaction of two solitons. 
format  Default Thesis 
id  rrarticle9374885 
institution  Loughborough University 
publishDate  1999 
record_format  Figshare 
spelling  rrarticle937488519990101T00:00:00Z Matrix Schrödinger equations and Darboux transformations V.M. Goncharenko (7158659) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified This thesis contains the matrix generalisations of some important results known in the theory of the scalar Schrödinger operators. In the first part we discuss the onedimensional matrix Schrodinger equations in complex domain. The main results here are the local criteria for the Schrödinger operators to have trivial monodromy and a matrix generalisation of the wellknown DuistermaatGrünbaum theorem giving the description of such operators in terms of Darboux transformations. In the second part we consider Dintegrable matrix Schrodinger operators in many dimensions. The local criteria on singularities of such operators are found and new examples are constructed. In the last chapter we discuss the soliton solutions of the matrix KdV equations and study the interaction of two solitons. 19990101T00:00:00Z Text Thesis 2134/28007 https://figshare.com/articles/thesis/Matrix_Schr_dinger_equations_and_Darboux_transformations/9374885 CC BYNCND 2.5 
spellingShingle  Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified V.M. Goncharenko Matrix Schrödinger equations and Darboux transformations 
title  Matrix Schrödinger equations and Darboux transformations 
title_full  Matrix Schrödinger equations and Darboux transformations 
title_fullStr  Matrix Schrödinger equations and Darboux transformations 
title_full_unstemmed  Matrix Schrödinger equations and Darboux transformations 
title_short  Matrix Schrödinger equations and Darboux transformations 
title_sort  matrix schrödinger equations and darboux transformations 
topic  Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified 
url  https://hdl.handle.net/2134/28007 