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Nonlinear superposition formulae of the Itô equation and a model equation for shallow water waves. (English) Zbl 0727.60126
Summary: Nonlinear superposition formulae of the Itô equation and a model equation for shallow water waves are proved under certain conditions. Some particular solutions of the Itô equation are obtained as illustrative application of the obtained nonlinear superposition formula.
MSC:
60K40Physical applications of random processes
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
60H99Stochastic analysis