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Charged solitons in branched conducting polymers
摘要： We consider the dynamics of charged solitons in branched conducting polymers, such as, e.g., trans-polyacetylene. An effective model based on the sine-Gordon equation on metric graphs is used for computing the charge transport and scattering of charge carriers at the polymer branching points. The condition for the ballistic charge carrier transport is revealed.
关键词： metric graphs,charged solitons,charge transport,branched conducting polymers,ballistic transport,sine-Gordon equation
更新于2025-09-23 15:21:21
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[IEEE 2018 Days on Diffraction (DD) - St.Petersburg, Russia (2018.6.4-2018.6.8)] 2018 Days on Diffraction (DD) - Complex representation of general solution of equations for nonlinear model of plane deformation of crystal media with a complex lattice
摘要： Complex representation of general solution of the nonlinear equations for deformation of crystal media with a complex lattice is given for a case of plane deformation. Expressions for acoustic and optical modes, as well as for tensors of macro- and microdeformations are obtained having applied arbitrary functions of a complex variable. They are similar to the Kolosov–Muskhelishvili formulas in the presence of bulk sources. In the nonlinear model, a role of bulk sources is played by microshifts us along a vector of the inverse lattice. The value us is found from the solution of a nonlinear equation of sine-Gordon type. The obtained complex representations of the general solution of the nonlinear equations allows us to apply the theory of functions of a complex variable to the solution of speci?c problems of the plane deformation theory.
关键词： sine-Gordon equation,crystal media,plane deformation,nonlinear model,complex representation
更新于2025-09-09 09:28:46
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Propagation of few-cycle pulses in a nonlinear medium and an integrable generalization of the sine-Gordon equation
摘要： The generalized sine-Gordon equation is obtained under the theoretical investigation of interaction of few-cycle pulses in a nonlinear medium modeled by a set of four-level atoms. This equation is derived without the use of the slowly varying envelope approximation and is shown to be integrable in the frameworks of the inverse scattering transformation method. Its solutions describing the propagation of the solitons and breathers and their interaction are investigated. In the case of different signs of the parameters of the equation considered, it is revealed, in particular, that the collision of solitons with opposite polarities can lead to an appearance of the short-living pulse having extraordinarily large amplitude, whose dynamics is similar to that of rogue waves. Also, the solitons of “rectangular” form and the breathers with rectangular oscillations exist in the case of the same signs of the parameters.
关键词： few-cycle pulses,generalized sine-Gordon equation,rogue waves,breathers,solitons,nonlinear medium
更新于2025-09-09 09:28:46