The Inverse Scattering Transform

Arthur Timmer, double bachelor project mathematics - physics, 2017. Supervisor of the physics part: Rudolf Sprik


  1. Introduction
  2. Inverse scattering transform method
    1. The direct scattering problem
      • Jost solutions, Picard method, existence, analytical properties, reflection and transmission coefficients, discrete spectrum, scattering data
    2. The inverse scattering problem
      • The Gelfand-Levitan-Marchenko equation, time evolution of the scattering data
  3. Inversion Imagin in Transmission Lines
    1. Transmission line model
    2. From the Telegrapher's equations to a Zhakarov-Shabat system
    3. The relation between the two reflection coefficients
    4. Inverse scattering solution
    5. Experimental validation
  4. Conclusion, outlook and suggestions