Investigation of double dispersive waves in nonlinear elastic inhomogeneous Murnaghan’s rod

Abstract

In this work, we retrieve a series of new wave solutions of the double dispersive equation that describes the nonlinear wave propagation in the elastic inhomogeneous Murnaghan’s rod by applying a novel integration norm known as the Sardar sub-equation method (SSEM). The solutions recovered by this method can be categorized as topological, non-topological, combo topological–non-topological, periodic and mixed periodic, singular and mixed singular solutions. In addition, by allotting different values to parameters, the physical movements of attained solutions are shown by plotting the 3D, 2D and contour graphs. On the basis of achieved results, we may claim that the proposed computational method is direct, dynamics, well organized, and will be useful for solving the more complicated nonlinear problems in diverse areas together with symbolic computations, especially in engineering and applied sciences.

Bifurcation analysis and soliton solutions to the doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

“…Alharthi et al 38 have examined wave solutions of the DD model using the modified generalized exponential rational function method and the Jacobi elliptical finder method. Rehman et al 39 investigated wave solutions of the DD model, which characterizes nonlinear wave propagation in the EIMR, employing the Sardar sub-equation method. Younas et al 40 developed exact solutions for the DD model utilizing the new extended direct algebraic and generalized Kudryashov methods.…”

Bifurcation analysis of the soliton solutions to the Doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

“…Rehman et al [21] investigated wave solutions of the DDE model, which characterizes nonlinear wave propagation in the EIMR, employing the Sardar sub-equation method. Younas et al [22] developed exact solutions for the DDE model utilizing the new extended direct algebraic and generalized Kudryashov methods.…”

Analytical study of the propagation of nonlinear waves on a Murnaghan hyperelastic circular pipe

“…In fact, this area of study is incomplete without the mention of the contributions of notable researchers like Newton, Hooks, Love, Rayleigh, Stoneley, and Murnaghan among others; read the famous book of Achenbach on the propagation of waves in elastic solids [1] and the book by Ewing et al [2] on the dispersion of waves in elastic media. However, of particular interest in this study is the examination of waves in hyperelastic media; precisely, the Murnaghan's circular pipe [3][4][5]. Using Murnaghan submission [6], the corresponding Cauchy-Green strain tensor takes into consideration the material nonlinearity that presides over the propagation of waves in hyperelastic structure; read Usman and Zaman [7] for the unambiguous expressions for the associated nonlinear strain and Murnaghan potential tensors in rectangular coordinates, respectively.…”