1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity
Abstract This paper obtains the 1-soliton solution of the Jaulent–Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence.
N-Fold Darboux Transformation of the Jaulent-Miodek Equation
In this paper, based on the Lax pair of the Jaulent-Miodek spectral problem, we construct the Darboux transformation of the Jaulent-Miodek Equation. Then from a trivial solution, we get the exact solutions of the Jaulent-Miodek Equation. We obtain a kink-type soliton and a bell-kink-type soliton. Particularly, we obtain the exact solutions which describe the elastic-inelastic-interaction coexistence phenomenon.
An anionic shell shields a cationic core allowing for uptake and release of polyelectrolytes within core-shell responsive microgels.
To realize carriers for drug delivery, cationic containers are required for anionic guests. Nevertheless, the toxicity of cationic carriers limits their practical use. In this study, we investigate a model system of polyampholyte N-isopropylacrylamide (NIPAM)-based microgels with a cationic core and an anionic shell to study whether the presence of a negative shell allows the cationic core to be shielded while still enabling the uptake and release of the anionic guest polyelectrolytes. These microgels are loaded with polystyrene sulfonate of different molecular weights to investigate the influence of their chain length on the uptake and release process. By means of small-angle neutron scattering, we evaluate the spatial distribution of polystyrene sulfonate within the microgels. The guest molecules are located in different parts of the core-shell microgels depending on their size. By combining these scattering results with UV-vis spectroscopy, electrophoretic mobility and potentiometric titrations we gain complementary results to investigate the uptake and release process of polyelectrolytes in polyampholyte core-shell microgels. Moreover, Brownian molecular dynamic simulations are performed to compare the experimental and theoretical results of this model. Our findings demonstrate that the presence of a shell still enables efficient uptake of guest molecules into the cationic core. These anionic guest molecules can be released through an anionic shell. Furthermore, the presence of a shell enhances the stability of the microgel-polyelectrolyte complexes with respect to the cationic precursor microgel alone.