A new approach to the Cauchy and Goursat problems for the nonlinear Wheeler–DeWitt equation
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We consider a nonlinear version of the Wheeler–DeWitt equation which was introduced by Cooper, Susskind, and Thorlacius in the context of two-dimensional quantum cosmology. We establish the existence of global solutions to the Cauchy problem and Goursat problems which, both, arise naturally in physics. Our method of proof is based on a nonlinear transformation of the Wheeler–DeWitt equation and on techniques introduced by Baez and collaborators and by Tsutsumi for nonlinear wave equations.
Mathematics Subject Classification83F05 74J30 83C47