Qualitative analysis and wave propagation of the nonlinear model for low-pass electrical transmission lines
Muneerah Al Nuwairan, A. A. Elmandouh
Abstract
Abstract This paper studies a nonlinear partial differential equation governing wave propagation in nonlinear low-pass electrical transmission. A travelling wave transformation is used to convert this equation into a 2D dynamical system which is proved to be a Hamiltonian system. Based on qualitative theory of the dynamical systems, a comprehensive qualitative study of bifurcation and phase portrait for this system is carried. We construct some new traveling wave solutions and they are graphically clarified.
Topics & Concepts
Phase portraitNonlinear systemBifurcationPartial differential equationPhysicsQualitative analysisTraveling waveWave propagationElectric power transmissionBifurcation theoryTransformation (genetics)Dynamical systems theoryMathematical analysisClassical mechanicsMathematicsOpticsElectrical engineeringQuantum mechanicsEngineeringQualitative researchChemistrySociologyGeneSocial scienceBiochemistryNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum chaos and dynamical systems