Dispersive shock waves propagating in the cubic-quintic derivative nonlinear Schrödinger equation

The propagation of a dispersive shock wave is studied in a quintic-derivative nonlinear Schrödinger (Q-DNLS) equation, which may describe, for example, the wave propagation on a discrete electrical transmission line. It is shown that a physical system described by a Q-DNLS equation without a dissipative term may support the propagation of shock waves. The influence of the derivative nonlinearity terms on the shock is analyzed. Using the found exact shock solutions of the Q-DNLS equation as the initial input signal, we investigate numerically the spatiotemporal stability of the shock signal in the network.