$q$-Boson in Quantum Integrable Systems

$q$-bosonic realization of the underlying Yang–Baxter algebra is identified for a series of quantum integrable systems, including some new models like two-mode $q$-bosonic model leading to a coupled two-component derivative NLS model, wide range of $q$-deformed matter-radiation models, $q$-anyon model etc. Result on a new exactly solvable interacting anyon gas, linked to $q$-anyons on the lattice is reported.