Solutions and conservation laws of Benjamin–Bona–Mahony–Peregrine equation with power-law and dual power-law nonlinearities

In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions and soliton solutions. Subsequently, the conservation laws are derived for the underlying equations.     

Water affinity and permeability in membranes of alginate-Ca2+ containing poly(n-isopropylacrylamide)

Hydrogels based on semi-interpenetrating network (semi-IPN) combining alginate-Ca²⁺ (matrix) with poly(N-isopropyl acrylamide) (PNIPAAm) were prepared and characterized in order to determine their affinity to water and their permeability to orange II as a function of temperature. Membranes of these hydrogels were obtained by gelation of the aqueous solution of alginate and PNIPAAm by the addition of CaCl₂. The presence of PNIPAAm chains inside the hydrogels alters the water affinity when compared to the pure alginate-Ca²⁺ hydrogels. Although the water uptake capability decreases above 32 °C (Low Critical Solution Temperature (LCST) of PNIPAAm in water), no shrinking of the semi-IPN hydrogels during the phase separation of the PNIPAAm was observed. The permeability of orange II as a function of temperature decreases at 32 °C and shows a dependence on the molar mass of the alginate. The partition coefficient of orange II in the hydrogel membrane, relative to water, decreases by increasing the temperature and its permeability follows a similar behavior. It was proposed that above the LCST of PNIPAAm the Alginate-Ca²⁺ networks mechanically support the collapsed PNIPAAm chains and the diffusion of orange II is minimized. The collapsing process may be followed by the formation of a complex between the carboxylic side groups of alginate and –NH–R groups of PNIPAAm. It would expose the isopropyl groups of PNIPAAm chains, providing a hydrophobic environment that minimizes the interaction between the dye and the polymeric matrix.     

The computational complexity of the criticality problems in a network with interval activity times

The paper analyzes the criticality in a network with interval activities duration times. A natural generalization of the criticality notion (for a path, an activity and an event) for the case of network with interval activity duration times is given. The computation complexity of five problems linked to the introduced criticality notion is presented.     

Explicit solutions and Darboux transformations of a generalized D-Kaup–Newell hierarchy

Nonlinear Dynamics - Darboux and Bäcklund transformations on integrable couplings are formulated and generalized. The generalization of the theory pertains to spectral problems where the...