Solitons exist in field theories with discrete vacua in flat two-dimensional Minkowski space. In our work, we are able for the first time to find analytic soliton solutions for specific values of the parameters for a generalization of the Ginzburg-Landau model in Anti-de-Sitter space. Using perturbation theory we show solutions continue to exist for parameter values close to these specific values. Further, acceptable numeric solutions exist for general values of the parameters. All of this supports the conclusion that soliton solutions to the equation of motion in Anti-de-Sitter 1+1 space exist for all values of the given parameters.
Schroeder, Daniel P., "Soliton Solutions in Anti-de-Sitter Space" (2007). Honors Projects. Paper 3.
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