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The nonlocal residual symmetries of a generalized Broer–Kaup–Kupershmidt system are constructed using the truncated Painlevé expansion. By considering appropriate potential variables, these nonlocal symmetries are localized into Lie point symmetries by prolonging the generalized Broer–Kaup–Kupershmidt system to an enlarged system. Moreover, multiple residual symmetries of the studied system are derived, their localization is performed, and the N-th Bäcklund transformation theorem is presented. Furthermore, some exact interaction solutions between solitons and various kinds of nonlinear waves are formulated in view of the new consistent tanh expansion method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Lie group formalism for the time fractional generalized nonlinear Broer–Kaup system in the sense of Riemann–Liouville fractional partial derivative. The Lie algebra corresponding to the symmetry groups in which the studied equation remains invariant is established, and the similarity reductions are performed. Next, based on the invariant subspace method as well as the power series method, including the convergence analysis, some exact solutions of the time fractional generalized Broer–Kaup system and its standard form are derived. Moreover, in order to show the dynamical behavior and the impact of the fractional order on the profile of solutions, some figures in 2D and 3D have been depicted. Finally, in accordance with the nonlinear self-adjointness property, conservation laws are successfully formulated using infinitesimal symmetries. [ABSTRACT FROM AUTHOR]

In this paper, the Lie symmetry group method is employed to study the time fractional generalized advection–diffusion equation. The Lie symmetry algebra classification is established by considering three different cases. Next, the similarity reductions are performed, and some solutions including invariants are derived. Finally, conservation laws are successfully constructed using the symmetry generators. [ABSTRACT FROM AUTHOR]

Polymer/clay-based composites were prepared via solution intercalation method using natural clay and poly (ethylene) glycol (PEG4000) as organic dispersed phase. The present work consists of studying the effect of PEG content on the hybrids surface morphology, thermal stability and thermophysical properties. On the other hand, the TGA data and the measured thermophysical properties are, respectively, fitted with a logistic-like laws and virial expansions for different polymer contents. The results showed that the experimental data agree with the proposed theoretical models. Furthermore, the incorporation of the PEG chains into the clay matrix improves both the thermal stability and thermal characteristics of the raw clay. The thermophysical properties data showed that the elaborated hybrid acts as good thermal insulator for polymer contents higher than 2.5 % . Finally, the resulting clay-based composite showed not only interesting characteristics in terms of insulation, but also satisfies both economic and environmental requirements. [ABSTRACT FROM AUTHOR]

In this paper, we apply the Lie symmetry analysis method for a time fractional perturbed standard KdV equation in the stationary coordinate (FPSKdV). The constructed symmetry generators are used to reduce the studied time fractional equation to a nonlinear fractional ordinary differential equation. With Erdélyi-Kober fractional operator, the reduced equation is solved with an explicit power series method. The constructing of its conservation laws is in order. [ABSTRACT FROM AUTHOR]