Abstract
New Broer–Kaup type systems of hydrodynamic equations are derived from the derivative reaction–diffusion systems arising in SL(2,R) Kaup–Newell hierarchy, represented in the non-Madelung hydrodynamic form. A relation with the problem of chiral solitons in quantum potential as a dimensional reduction of 2+1 dimensional Chern–Simons theory for anyons is shown. By the Hirota bilinear method, soliton solutions are constructed and the resonant character of soliton interaction is found.
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