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Nonlinear algebra and Bogoliubov’s recursion. (English. Russian original) Zbl 1150.81014
Theor. Math. Phys. 154, No. 2, 270-293 (2008); translation from Teor. Mat. Fiz. 154, No. 2, 316-343 (2008).
Summary: We give many examples of applying Bogoliubov’s forest formula to iterative solutions of various nonlinear equations. The same formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field theory.

MSC:
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81R15 Operator algebra methods applied to problems in quantum theory
35Q55 NLS equations (nonlinear Schrödinger equations)
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