Factorization of the Non-Stationary Schrödinger Operator
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We consider a factorization of the non-stationary Schrödinger operator based on the parabolic Dirac operator introduced by Cerejeiras, Kähler and Sommen. Based on the fundamental solution for the parabolic Dirac operators, we shall construct appropriated Teodurescu and Cauchy-Bitsadze operators. Afterwards we will describe how to solve the nonlinear Schrödinger equation using Banach fixed point theorem.
Mathematics Subject Classification (2000).Primary 30G35 Secondary 35A08, 15A66
Keywords.Nonlinear PDE’s parabolic Dirac operators iterative methods
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