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The Inverse Scattering Transform
Arthur Timmer, double bachelor project mathematics - physics, 2017. Supervisor of the physics part:
Rudolf Sprik
Outline
Introduction
Inverse scattering transform method
The direct scattering problem
Jost solutions, Picard method, existence, analytical properties, reflection and transmission coefficients, discrete spectrum, scattering data
The inverse scattering problem
The Gelfand-Levitan-Marchenko equation, time evolution of the scattering data
Inversion Imagin in Transmission Lines
Transmission line model
From the Telegrapher's equations to a Zhakarov-Shabat system
The relation between the two reflection coefficients
Inverse scattering solution
Experimental validation
Conclusion, outlook and suggestions