<p>Dynamics of nonlinear and supernonlinear electric signals are investigated in nonlinear electrical transmission lines (NETL). An evolution equation is derived employing Kirchhoff's current and voltage laws so as to describe the propagation of nonlinear electric signals in the NETL. Using a traveling wave transformation the dynamical system is obtained from the evolution equation for the signals. Phase plane analysis is used in the dynamical system for studying different kinds of nonlinear signals in the NETL. Additionally, periodic signals, solitary signals and superperiodic signals are obtained corresponding to periodic orbits, homoclinic orbits and superperiodic orbits obtained in the phase portraits. Effects of the different physical parameters, such as, speed of traveling signal (<i>v</i>), spacing (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11082_2025_8334_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta _1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>) between two adjacent portions in the propagation direction of the electric signal, spacing (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11082_2025_8334_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta _2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>) between two adjacent portion in the transverse direction of the propagation of the electric signal, inductance (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11082_2025_8334_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$L_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>) in series branch and inductance (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11082_2025_8334_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$L_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>) are presented on periodic, superperiodic and solitary electric signals. Analytical forms of the solitary electric signals of peak and valley types are obtained. Furthermore, linear stability analysis of the signals is conducted in the presence of a small voltage perturbation using linearization technique.</p>

Dynamics of nonlinear and supernonlinear electric signals in a transmission line

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发表日期：

2025年9月15日

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Dickcha Pradhan,
Lamberto Rondoni,
Asit Saha

摘要

Dynamics of nonlinear and supernonlinear electric signals are investigated in nonlinear electrical transmission lines (NETL). An evolution equation is derived employing Kirchhoff's current and voltage laws so as to describe the propagation of nonlinear electric signals in the NETL. Using a traveling wave transformation the dynamical system is obtained from the evolution equation for the signals. Phase plane analysis is used in the dynamical system for studying different kinds of nonlinear signals in the NETL. Additionally, periodic signals, solitary signals and superperiodic signals are obtained corresponding to periodic orbits, homoclinic orbits and superperiodic orbits obtained in the phase portraits. Effects of the different physical parameters, such as, speed of traveling signal (v), spacing ( $\delta _1$ $δ_{1}$ ) between two adjacent portions in the propagation direction of the electric signal, spacing ( $\delta _2$ $δ_{2}$ ) between two adjacent portion in the transverse direction of the propagation of the electric signal, inductance ( $L_1$ $L_{1}$ ) in series branch and inductance ( $L_2$ $L_{2}$ ) are presented on periodic, superperiodic and solitary electric signals. Analytical forms of the solitary electric signals of peak and valley types are obtained. Furthermore, linear stability analysis of the signals is conducted in the presence of a small voltage perturbation using linearization technique.