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We propose an exactly solvable model of one-dimensional anyons with competing$\delta$-function and derivative $\delta$-function interaction potentials. TheBethe ansatz equations are derived in terms of the $N$-particle sector for thequantum anyonic field model of the generalized derivative nonlinearSchr\"{o}dinger equation. This more general anyon model exhibits richer physicsthan that of the recently studied one-dimensional model of $\delta$-functioninteracting anyons. We show that the anyonic signature is inextricably relatedto the velocities of the colliding particles and the pairwise dynamicalinteraction between particles.

One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials