Abstract
The nonlinear dispersive wave equation inside the cylindrical elastic rod is derived by applying the Navier–Bernoulli hypothesis and Love’s relation. The elastic rod is assumed to be composed of the Murnaghan’s materials such as Lamé’s coefficient, Poisson ratio and constitutive constant which are compressible in nature. In this research paper we apply the two integral architectures namely extended sine–Gordon method and modified exponential function method to study the dispersive wave and solve for the solitons and their classifications. The topological (or) dark soliton, compound topological–non-topological (bright–dark) solitons are obtained by extended sine–Gordon method. The soliton like and singular periodic solutions are obtained by modified exponential function method. The existence of the number of solutions are proved with respect to the linear equation obtained by balancing principle. The related two and three dimensional graphs are simulated and drawn to show the complex structures.
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