Abstract
Collisions of two pulsed signals in a medium with modular (M) nonlinearity and a special relaxation law are investigated. The processes are described by an integro-differential equation, the kernel of which is nonzero in a finite time interval. It is believed that within this interval, the “memory of the medium” is constant, but outside it, it vanishes. For this model, the analysis is reduced to solving a simple differential-difference equation, whereas the volume of computations is significantly reduced. The phenomena accompanying pulse collisions of are described: nonlinear mutual attenuation, annihilation, and signal broadening with time. The effect of the signal parameters and properties of the medium on these processes is explained. The collision of two modular solitons described by the Korteweg–de Vries M-equation is considered. It is shown that, by using this model, the interaction may differ from the usual behavior of solitons, revealing an analogy with elastic particle interaction.
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