Является Ли Кинковое Решение Нелинейного Уравнения Клейна--Гордона Солитоном?

Abstract

The possibility of the existence of soliton solutions of the generalized sine-Gordon equation (also referred to as Kryuchkov-Kukhar equation (KKeq)) has been investigated numerically. This equation describes the propagation of electromagnetic waves in a graphene superlattice. The computational errors associated with the implicit form of the expression defining the kink solution of the considering equation are estimated. The differences between the forms before and after the collision of pulses, propagating towards each other, are estimated. On the basis of the obtained results it is concluded that the considered kink solution is not a soliton.