Application of a new functional expansion to the cubic anharmonic oscillator
- 1 April 1982
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 23 (4) , 495-502
- https://doi.org/10.1063/1.525408
Abstract
A new representation of causal functionals is introduced which makes use of noncommutative generating power series and iterated integrals. This technique allows the solutions of nonlinear differential equations with forcing terms to be obtained in a simple and natural way. It generalizes some properties of Fourier and Laplace transforms to nonlinear systems and leads to effective computations of various perturbative expansions. Illustrations by means of the cubic anharmonic oscillator are given in both the deterministic and the stochastic cases.Keywords
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