The current study examines the special class of a generalized reaction-advection-diffusion dynamical model that is called the system of coupled Burger’s equations. This system plays a vital role in the essential areas of physics, including fluid dynamics and acoustics. Moreover, two promising analytical integration schemes are employed for the study; in addition to the deployment of an efficient variant of the eminent Adomian decomposition method. Three sets of analytical wave solutions are revealed, including exponential, periodic, and dark-singular wave solutions; while an amazed rapidly convergent approximate solution is acquired on the other hand. At the end, certain graphical illustrations and tables are provided to support the reported analytical and numerical results. No doubt, the present study is set to bridge the existing gap between the analytical and numerical approaches with regard to the solution validity of various models of mathematical physics.

The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency.

The present manuscript focuses on the study of surface wave propagation in a rotating coated viscoelastic half-space and its response to external forces comprised of the magnetic field and gravitational forces. A celebrated normal mode analysis procedure is adopted as the methodology of interest for its high level of efficiency in the literature. The analytically obtained frequency equation is analyzed for certain scenarios of curiosity, in addition to the determination of the resulting displacements and stresses. Moreover, certain physical data of relevance with the viscoelasticity index of unity are considered for the numerical simulations. As for the findings, the presented graphical illustrations showed that both the magnetic field and rotation positively accelerated the dispersion of surface waves in the coated half-space, while the obtained approximate fields in the half-space are found to be oscillatory as they steadily move towards the limiting point.