Solitons are an important part of field theory, that feature discrete vacua. In this paper, we start with a specific soliton potential to study in depth. Utilizing perturbation theory, in both real and imaginary space, we study the scalar potentials in Minkowski and AdS space. Using supersymmetry and shape invariance, we analytically solve the soliton normal mode equations and determine their frequency spectra. Furthermore, reversing the methods used, we are able to work backwards and find more soliton potentials that are in the same family as our original one.
Webster, Matthew, "Supersymmetry and Shape Invariance: Soliton Excitation Spectra in Anti-de-Sitter Space" (2009). Physics and Astronomy Honors Projects. Paper 10.
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