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Modular “Solitons”: Mutual Absorption and Annihilation in Dissipative Media
Acoustical Physics ( IF 0.8 ) Pub Date : 2020-05-19 , DOI: 10.1134/s1063771020030070
O. A. Vasilieva , O. V. Rudenko

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.


中文翻译:

模块化“孤子”:耗散介质中的相互吸收和An灭

摘要

研究了具有模块化(M)非线性和特殊松弛定律的介质中两个脉冲信号的碰撞。这些过程由整数微分方程描述,该整数微分方程的内核在有限的时间间隔内不为零。可以相信,在此间隔内,“介质的内存”是恒定的,但在其外部,则消失了。对于此模型,分析被简化为求解一个简单的差分方程,而计算量则显着减少。描述了伴随脉冲碰撞的现象:非线性相互衰减,an灭和信号随时间变宽。解释了信号参数和介质属性对这些过程的影响。考虑了由Korteweg-de Vries M方程描述的两个模块化孤子的碰撞。
更新日期:2020-05-19
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