A Relaxing Medium with “Linearly Weakening Memory”: Evolution of Intense Pulses

Abstract

The evolution of pulsed signals in a quadratically nonlinear medium with a special relaxation law is studied. It is believed that the “memory of the medium” weakens according to a linear law and becomes zero within a finite time. Instead of standard integro-differential equations with exponential or fractional power kernels, a model of a medium with a finite memory time is used here. For this model, analysis of complex integro-differential equations reduces to solving a differential-difference equation; at the same time, the amount of calculations is appreciably curtailed. The processes accompanying pulse evolution—shock front formation, nonlinear attenuation, and signal spreading with time—are described. The influence of the relaxation time on these processes is explained.