Engineering breathers in a weakly dissipative nonlinear electrical transmission line

Emmanuel Kengne and Ahmed Lakhssassi

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: We study analytically the generation of breather voltages in a nonlinear electrical transmission line when the dissipative effects are taken into consideration. Focusing on the case of weak dissipation, we apply the reductive perturbation technique in the semidiscrete limit to show that the propagation of weakly nonlinear modulated waves in the network system is modeled by a distributed nonlinear Schrödinger equation. The baseband modulational instability, a phenomenon responsible of simultaneously formation of both soliton and rogue wave, is investigated and the analytical expression for the modulational gain spectrum is derived. Under the condition of the baseband modulational instability, we derive approximate analytical localized wave solutions of model equation. Based on those approximate solutions, we prove that our network system support the propagation of breathers embedded on a vanishing/nonvanishing continuous wave background. We show that, despite the presence of dissipative elements, the propagation of electrical breathers remains possible in the case of weak dissipations. More interestingly, our results show that in the domain where the network may exhibit baseband modulational instability, effects of dissipative losses in the shunt branch are dominated by those in series branch. Also, some of obtained approximate solutions are found to be useful for describing the compression of breather waves propagating in the network under consideration. The numerical results perfectly match the analytical predictions.

Keywords: Distributed nonlinear Schrödinger equation; Breathers; Baseband modulational instability criterion; Electrical transmission line (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008258

DOI: 10.1016/j.chaos.2026.118684

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