Innovative solutions for lossy nonlinear transmission lines model using a modified extended mapping approach with...

Area of Science:

• Nonlinear Dynamics
• Mathematical Physics
• Electrical Engineering

Background:

• Nonlinear electrical transmission lines (NLETLs) are crucial for signal propagation.
• Fractional calculus offers a more generalized approach to modeling complex systems.
• Soliton solutions represent stable, localized waves in nonlinear systems.

Purpose of the Study:

• To investigate exact analytical soliton solutions for a conformable fractional lossy nonlinear electrical transmission line (Loss-NLETL) model.
• To explore the influence of fractional order on soliton behavior.
• To demonstrate the efficacy of the Modified Extended Mapping (Mod-EM) technique.

Main Methods:

• The Modified Extended Mapping (Mod-EM) technique was employed.
• Conformable fractional derivatives were incorporated into the NLETL model.
• Exact analytical solutions were derived and visualized using 2D, 3D, and density plots.

Main Results:

• A wide array of exact analytical solutions were obtained, including novel composite, hyperbolic, trigonometric, and Jacobi elliptic wave solutions.
• The study identified diverse soliton structures such as dark solitons and kink-rational hyperbolic components.
• Parametric analysis revealed the impact of fractional order on waveform evolution.

Conclusions:

• The Mod-EM technique is effective for generating diverse soliton solutions in complex fractional nonlinear systems.
• The obtained solutions offer new insights into wave propagation in Loss-NLETLs.
• Results have potential implications for advanced applications in applied physics and electrical engineering.