Generalized travelling wave solutions for hyperbolic chemotaxis PDEs

• Utilization of symmetry results to generate generalized travelling wave solutions.
• Explicit solutions demonstrated for the first time when diffusion is considered.
• Full analysis of the boundedness conditions of the solutions.

The chemotaxis of E. coli can be modelled via a system of partial differential equations. We apply group theoretical techniques to investigate the existence of travelling wave solutions for the hyperbolic chemotaxis model. Unlike previous approaches, we allow for the presence of the diffusivity terms, thereby maintaining the intrinsic second order terms of the diffusion equations in the model. We show, in the case of non starvation, that this model is still tractable. Explicit travelling wave solutions are determined.