Riemann solutions and wave interactions for a hyperbolic system derived from the steady 2D Helmholtz equation under a paraxial assumption

Abstract

Two kinds of exact Riemann solutions for a hyperbolic system arising from the steady 2D Helmholtz equation under a paraxial assumption are constructively achieved by using either delta shock wave or contact-vacuum-contact composite wave, which depends on the ordering relation between the left and right initial velocities. Moreover, the interaction between delta shock wave and contact-vacuum-contact composite wave is carefully explored by considering the initial data in three pieces separated by two jump discontinuities.