Abstract
This study investigates the analytical solitary wave solutions of the nonlinear Sine–Gordon (SG) system by using two recent computational (Khater II and novel Kudryashov) schemes. The studied model is used as a model for various wave phenomena, including the propagation of dislocations in crystals, phase differences across Josephson junctions, torsion waves in strings and pendula, and waves along lipid membranes. It was already studied in the nineteenth century in connection with the theory of pseudospherical surfaces. The quantum version is used as a simple model for solid–state excitations. The solitonic property of the constructed solutions is also explained through some distinct graphs in two-, three-dimensional, contour, and polar plots. The stability property of the obtained soliton wave solutions is discussed based on the Hamiltonian system’s characterizations.
Published Version
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