Abstract.
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.
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The research of the first author was (partially) supported by Unidade de Investigação “Matemática e Aplicações” of the University of Aveiro. The work of the second author is supported by Fundação para a Ciência e a Tecnologia via the PhD-grant SFRH/BD/22646/2005.
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Cerejeiras, P., Vieira, N. Factorization of the Non-Stationary Schrödinger Operator. AACA 17, 331–341 (2007). https://doi.org/10.1007/s00006-007-0039-6
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DOI: https://doi.org/10.1007/s00006-007-0039-6