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Doctoral Thesis
DOI
https://doi.org/10.11606/T.43.1984.tde-28022014-101333
Document
Author
Full name
Helena Maria Avila de Castro
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1984
Supervisor
Committee
Wreszinski, Walter Felipe (President)
Braga, Carmen Lys Ribeiro
Escobar, Bruto Max Pimentel
Henry, Daniel Bauman
Ventura, Ivan
Title in Portuguese
Resultados matemáticos sobre o método de espalhamento inverso.
Keywords in Portuguese
Método de espalhamento inverso
Abstract in Portuguese
Neste trabalho são apresentados alguns resultados matemáticos relevantes para a aplicação do método de espalhamento inverso à resolução de uma classe de equações de evolução não-lineares. É demonstrada a propriedade isoespectral para certas famílias de operadores lineares não auto-adjuntos. Esta propriedade tem um papel central na aplicação do método acima a equações de evolução não-lineares de interesse físico, tais como a equação de sine-Gordon e a equação de Schrödinger não-linear. É feito também, uma teoria de espalhamento inverso rigorosa para sistemas do tipo Zakharov-Shabat, o que inclui uma análise qualitativa do espectro de operadores deste tipo.
Title in English
Mathematical results about the method of inverse scattering.
Keywords in English
Inverse scattering method
Abstract in English
This Thesis presents some mathematical results relevant in applications of the inverse scattering transform to the solution of a class of non-linear evolution equations. First, it is shown that certain families of non-selfadjoint linear operators have the isospectral property, which is fundamental for the above applications. These families include various operators related to no-linear equations of great physical interest, such as the sine-Gordon and the non-linear Schrödinger equations. In the sequel, a rigorous inverse scattering theory, including a qualitative spectral analysis, is developed for systems of Zakharov-Shabat type.
 
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RE45423Castro.pdf (23.81 Mbytes)
Publishing Date
2014-02-28
 
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