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This study examines the dispersion of elastic waves in a strongly inhomogeneous three-layered plate resting on a Winkler elastic foundation in the presence of imperfect interfacial conditions alongside a stress-free upper face. The propagation of elastic waves in the plate is governed by the two-dimensional anti-plane shear motion. The asymptotic technique is employed for the analysis. The exact dispersion relation and the overall cut-off frequency are determined. Within the long-wave low-frequency region, the shortened polynomial dispersion relation corresponding to the exact dispersion relation has been computed and studied for a particular material contrast. The associated one-dimensional equations of motions are also derived in approximate forms for perfect interface as a case of interest. Finally, according to the findings of this investigation, the obtained approximate equations of motions for a three-layered plate remain valid over the entire low-frequency spectrum even in presence of an elastic foundation. We also examined the variational impacts of the dimensionless Winkler elastic foundation parameter G and the interface imperfect parameter γ on the dispersion branch of harmonic waves. Furthermore, to assure the long-wave low-frequency range, the numerical simulations and graphical visualization are presented by utilizing certain physical data.

This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

The present paper investigates the propagation and dispersion of elastic surface waves in an asymmetric inhomogeneous isotropic three-layered plate in the presence of magnetic field and rotational effects. The skin layers are exposed to an external magnetic field force while the core layer is assumed to be in a rotational frame of reference, which are perfectly bounded together with free-ends conditions. The resultant displacements and shear stresses in the respective layers are derived analytically together with the general dispersion relation. Further, the general dispersion relation is analyzed for some physical cases of interest. Finally, the effects of the magnetic field, rotation, and electric field on the propagation and dispersion of the present model are presented graphically.

The fractional partial differential equations have wide applications in science and engineering. In this paper, the Kudryashov techniques were utilized to obtain an exact solution of both fractional generalized equal width (GEW)-Burgers and classical GEW-Burgers equations. The general analytical solutions of the two partial differential equations are constructed for n>1. The graphical representation of the solutions is given in comparison with some previous results in the literature. The advantages and disadvantages of the method were listed.

In the present paper, the two-dimensional quantum Zakharov-Kuznetsov (QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations.

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