It has long been recognized that certain bacterial groups exhibit cooperative behavioral patterns. Bacteria accomplish such communication via exchange of extracellular signaling molecules called pheromones( autoinducer or quorum sensing molecules). As the bacterial culture grows, signal molecules are released into extracellular milieu accumulate, changing water fluidity. Under such threshold conditions swimming bacterial suspensions impose a coordinated water movement on a length scale of the order 10 to 100 micrometers compared with a bacterial size of the order of 3 micrometers.Here, we investigate the non-local hydrodynamics of the quorum state and pattern formation using forced Burgers equation with Kwak transformation. Such approach resulted in the conversion of the Burgers equation paradigm into a reaction-diffusion system. The examination of the dynamics of the quorum sensing system, both analytically as well as numerically result in similar long-time dynamical behaviour.