The stochastic integrable AKNS hierarchy

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Title: The stochastic integrable AKNS hierarchy
Authors: Arnaudon, A
Item Type: Working Paper
Abstract: We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose some properties of these equations and also briefly study a stochastic Camassa-Holm equation which reduces to a stochastic Hamiltonian system of peakons.
Copyright Statement: © The Author
Keywords: nlin.SI
Notes: First version, comments welcome!
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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