Intense Pulses in Relaxing Media with Limited “Memory Time,” Power-Law and Nonanalytic Nonlinearities

Abstract

Processes that accompany propagation of time-limited pulsed signals in a relaxing medium are investigated for the case of a nonlinear medium with power-law (quadratic or cubic) nonlinearity or nonanalytic nonlinearity (modular or quadratically cubic one). Instead of ordinary integro-differential equations with exponential or fractional-power kernels, a simplified model of a medium with finite “memory time” is used. Such a medium “remembers” its prehistory within a limited time interval, and the corresponding kernel of the integral term is nonzero only within a finite interval. For this model, the problem is reduced to solving a difference-differential equation, which considerably reduces the amount of calculations, as compared to the initial integral equation. The processes that accompany evolution of pulses, namely, the formation of compression and rarefaction shock fronts and the appearance of triangular and trapezoidal nonlinear structures, are described. Effect of relaxation time on these processes is revealed.