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(Al,In)GaN laser diodes show an intricate interplay of longitudinal mode competition and mode clustering. So far, modelling of these diodes has been restricted to rate equations, necessitating the input of a variety of phenomenological parameters. Here, we perform calculations based on the semiconductor Bloch equations which offer the chance of a full many-body calculation and microscopic determination of all parameters. In the current contribution, we restrict our calculations to basic mechanisms and use phenomenological parameters for numerical reasons. Even in this simple model, we are able to reproduce the mode rolling phenomena found in measurements and gain access to parameters not accessible in a rate equation model.