Interaction of Dirac δ$$ \delta $$‐Waves in the Inviscid Levine and Sleeman Chemotaxis Model

ABSTRACT This article investigates interactions of ‐shock waves in the inviscid Levine and Sleeman chemotaxis model , . The analysis employs a distributional product and a solution concept that extends the classical solution concept. The interactions are studied by solving a Cauchy problem corresponding to a Riemann problem with delta initial data in both state variables. For each state variable, the resulting solutions exhibit behaviour analogous to classical solitons.