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Compatibility Conditions and the Manifold of Solutions of some Nonlinear Cauchy‐Riemann System in Several Complex Variables
Author(s) -
Hayashi Yasuo
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921590111
Subject(s) - mathematics , cauchy–riemann equations , compatibility (geochemistry) , nonlinear system , initial value problem , mathematical analysis , factorization , pure mathematics , physics , geochemistry , algorithm , quantum mechanics , geology
The system of differential equationsIs studied. On the assumption that the system admits certain class of solutions, necessary conditions of compatibility are deduced, and by introducing some changes of variables the system is reduced to a single differential equation, then conversely by solving it, the formula giving all local solutions of the system is infered. The validity of the factorization theorem and the identity theorem for solutions in the class is also treated.