(Al,In)GaN laser diodes have various relevant applications, especially in projection systems for virtual and augmented reality devices and in optical communication, all requiring fast modulation. This corresponds to pulses in the nanosecond to microsecond range, where a rich longitudinal mode dynamics occurs. We investigate this spectral-temporal dynamics experimentally with a streak camera system and simulate it using a longitudinal multi-mode rate equation model. We observe an interplay of effects, which have been observed selectively, such as relaxation oscillations, mode competition and inhomogeneous pumping of multiple quantum wells. A mechanism is included in the simulations to model the red-shift of the gain spectrum due to the carrier density in the quantum wells exceeding threshold density, which is amplified by inhomogeneous pumping. Mode competition leads to spectral cycles of the active mode with a noticeable jitter, which is observed in single pulse measurements in comparison to multi pulse averaged measurements where blurring occurs. Here, some statistical behavior as well as repeating patterns are investigated at the same effect. Also thermal effects as laser diode self-heating are discussed and have been measured over six orders of magnitude in time.