Chiral resonant solitons in Chern–Simons theory and Broer–Kaup type new hydrodynamic systems

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.

► We reduce chiral solitons in quantum potential from Chern–Simons theory of anyons.
► We examine corresponding family of integrable resonant DNLS models.
► Models admit the second non-Madelung hydrodynamic representation.
► New hydrodynamic systems of the Broer–Kaup type are derived.
► Soliton interactions in these systems show the resonant character.