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Polynomial nonlinearities in differential equations. (English) Zbl 0606.34009
The first author and his collaborators have found solutions for nonlinear stochastic (or deterministic in the limiting case) differential equations involving polynomial nonlinearities. Using the first author’s $$A_ n$$ polynomials and recently developed methods of calculating these polynomials, it becomes very easy to write solutions for nonlinear terms such as $$y^ m$$ for positive integers m. The cases of negative integer m or even decimal powers will appear elsewhere.

##### MSC:
 34A34 Nonlinear ordinary differential equations and systems 34F05 Ordinary differential equations and systems with randomness
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##### References:
 [1] Adomian, G, Stochastic systems, (1983), Academic Press New York/London · Zbl 0504.60066 [2] Adomian, G, Nonlinear stochastic differential equations, J. math. anal. appl., 55, No. 1, 441-452, (1976) · Zbl 0351.60053 [3] Adomian, G; Sibul, L.H, Symmetrized solutions for nonlinear stochastic differential equations, Internat. J. math. math. sci., 4, No. 3, 529-542, (1981) · Zbl 0465.60057 [4] Adomian, G; Rach, R, Inversion of nonlinear stochastic operators, J. math. anal. appl., 91, No. 1, 39-46, (1983) · Zbl 0504.60066 [5] Rach, R, A convenient computational form for the Adomian polynomials, J. math. anal. appl., 102, No. 2, 415-419, (1984) · Zbl 0552.60061 [6] {\scG. Adomian}, “Stochastic Systems II,” to appear. · Zbl 0523.60056
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