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In this paper, the integrable (4 + 1)-dimensional Fokas equation is investigated. Exploiting a set of non-singular local multipliers, we present a set of local conservation laws for the equation. The nonlocally related partial differential equation (PDE) systems are found. Nine nonlocally related systems are discussed reveal thirty five interesting closed form solutions of the equation. These solutions contain different types of wave solutions, double soliton, multi-solitons, kink and periodic wave solutions. Some of the resulting solutions are graphically illustrated. Furthermore, we apply the sine-cosine method to find other traveling wave solutions for this equation. [ABSTRACT FROM AUTHOR]

Considering the importance of correctly understanding the dynamics of microstructure materials for their applications in related technologies, by eliminating the shortcomings and some overlooked physical concepts in the existing asymmetric elastic theories, we have presented an asymmetric elastodynamic model based on a $ U(1) $ U (1) gauge theory with quantum electrodynamics (QED) structure. Accordingly, we have shown that there is a correspondence between an elastic theory, which can explain the behavior of elastic waves within an asymmetric elastic medium and QED. More specific, we have indicated that the corresponding elastic wave equations are somehow analogous to QED ones. In this regard, by adding vibrational degrees of freedom and introducing a gauge property of the waves of displacement for the waves of rotation, we have generalized and modified the related Cosserat theory (CT) for an elastic environment. Thus on macro scales, the elastic waves can possess the QED treatment. This analogy provides a new paradigm of fermions and bosons. Also, from experimental point of view, we have shown that the behavior of elastic waves in a granular medium is equivalent to behavior of light in dispersive media, which can be explained using QED. Hence, contrary to the Cosserat and discrete models, this amended CT has qualitatively been indicated to be consistent with the corresponding empirical observations. [ABSTRACT FROM AUTHOR]

In this paper, analytic solutions and dynamic properties of a variety of Boussinesq-type equations are established via the complete discrimination system for polynomial method. All the existing single traveling wave solutions to these equations as well as some new solutions are shown, and the Hamiltonian and topological properties to these equations are also presented. Considering the significance of the Boussinesq-type equations, our results would have wide applications in ocean engineering and fluid mechanics, like describing and predicting the solitary and periodic waves in various shallow water models. [ABSTRACT FROM AUTHOR]

The paper studies the influence of the initial inhomogeneous thermal stresses on the dispersion of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder within the scope of the 3D linearized theory of elastic waves in initially stressed bodies. The initial static thermal stresses are determined within the scope of the uncoupled classical linear theory of thermo-elasticity and it is assumed that the temperature change in the cylinder is caused by the heating or cooling of the inner and outer surfaces of the cylinder. The discrete analytical solution method is employed for the solution to the corresponding equations of the wave propagation. Concrete numerical results are obtained for the cylinder, the materials of the layers of which are steel and aluminum, as well for the cylinder made of steel only. Numerical results on the influence of the initial inhomogeneous thermal stresses on the dispersion curves related to the first, second and third modes are presented and discussed. In particular, it is established that the cooling or the heating of the outer and inner surfaces of the bi-layered hollow cylinder influences the dispersion curves not only in the quantitative sense, but also in the qualitative sense. [ABSTRACT FROM AUTHOR]