AbstractScalar nonlinearities are operators of the form N(u) = 〈Au, u〉Bu, where A, B are linear operators, and 〈·,·〉 is the inner product in a Hilbert space ℋ︁. This paper reviews applications of scalar nonlinearities. We show that operators of the form N(u) are found in equations that describe phenomena of classical mechanics, open systems of quantum mechanics, and chemical physics.
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