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We investigate the boson-fermion duality relation for the case of quantumintegrable derivative $\delta$-function bose gas. In particular, we find out adual fermionic system with nonvanishing zero-range interaction for the simplestcase of two bosonic particles with derivative $\delta$-function interaction.The coupling constant of this dual fermionic system becomes inverselyproportional to the product of the coupling constant of its bosonic counterpartand the centre-of-mass momentum of the corresponding eigenfunction.

Fermionic dual of one-dimensional bosonic particles with derivative delta function potential