Interaction of short pulses in a 3 × 3 hyperbolic system

Abstract

This paper concerns the asymptotic behaviours of pulse-like solutions for a 3 × 3 semilinear hyperbolic system in the limit of short wavelength ε. When two pulses interact with each other, we construct a pulse-like approximate solution up to Ο(ε), at which order a new pulse appears. The existence of a solution to the 3 × 3 semilinear problem with the initial data being the interaction of two pulses in a domain independent of the wavelength is proved in the space of co-normal distributions. Meanwhile, we obtain that the error between this exact solution and the approximate solution is of Ο(ε2) as ε → 0, which rigorously shows that there are three pulses propagated after the interaction of two pulses for the 3 × 3 semilinear system.