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Exact Solution of Double<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>δ</mml:mi></mml:math>Function Bose Gas through an Interacting Anyon Gas
A 1D Bose gas interacting through $\ensuremath{\delta},{\ensuremath{\delta}}^{\ensuremath{'}}$ and double $\ensuremath{\delta}$ function potentials is shown to be equivalent to a $\ensuremath{\delta}$ anyon gas, allowing an exact Bethe ansatz solution. In the noninteracting limit, it describes an ideal gas with generalized exclusion statistics and solves some recent controversies.