Symmetries play an important role in solving partial differential equations. In this paper, the determining equations for a class of nonlinear partial differential equations with arbitrary order are considered. It is shown that the determining equations for the nonclassical reduction can be obtained by requiring the compatibility between the original equation and the invariant surface condition...

For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Bäcklund–Darboux transformations and the corresponding discrete system are considered for Kupershmidt’s super KdV equation....

Abstract The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. interaction between layers is taken into account due to van der Waals forces. investigation based on nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. effect Lorentz force Maxwell’s equations. go...

Building on a research framework based on the Theory of Reasoned Action (TRA), Innovation Diffusion Technology (IDT), and the Technology Adoption Model (TAM), we propose a model integrating compatibility, social influence, and perceived familiarity given the implicit uncertainty of personal cloud. Our model emphasizes the moderating effect of perceived familiarity on the relationships between b...

This paper discusses a new method for damage detection based on the most fundamental concept in continuum mechanics: strain compatibility. Compliance with this principle implies a deformed material is free from discontinuities, which are indicative of many types of structural damage. Therefore the principle of strain compatibility, in its ability to identify discontinuities, is very promising a...

The load partitioning between surface and bulk was studied by means of in-situ synchrotron energy dispersive diffraction in an SAF 2507 superduplex stainless steel having a strain hardened surface layer with compressive residual stresses. Two loading cycles with a peak tensile strain of 0.5% and 0.87%, respectively, were successively applied and the evolution of stresses in the respective const...

Experiments were done to assess the compatibility of nateglinide with selected excipients in the development of immediate release tablets of nateglinide by thermal and isothermal stress testing (IST) techniques. To evaluate the drug-excipient compatibility, different techniques such as differential scanning calorimetric (DSC) study, infra-red (IR) spectrophotometric study and isothermal stress ...

We use Hodge-type orthogonal decompositions for studying the compatibility equations of the displacement gradient and the linear strain with prescribed boundary displacements. We show that the displacement gradient is compatible if and only if for any equilibrated virtual first-Piola Kirchhoff stress tensor field, the virtual work done by the displacement gradient is equal to the virtual work d...