Collision of delta-waves in a turbulent model studied via a distribution product Original Research Article

By using a product of distributions, the existence and collision of soliton delta-waves for a singular perturbation of the Burgers conservative equation are established. We also prove that singular solitons under collision behave as in classical soliton collision (for example, as described by the Korteweg–de Vries equation). The impossibility of two delta-wave collisions for the inviscid Burgers conservative equation is also verified. The introduction is dedicated to a motivation for our study.