Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model. Specifically, we apply the approach to the nonlinear space–time fractional model leading the wave to spread in electrical transmission lines(s-tf ETL), the time fractional complex Schr?dinger(tfc S), and the space–time M-fractional Schr?dinger–Hirota(s-t M-f SH) models to verify the effectiveness of the proposed approach. The implementing of the introduced new technique based on the models provides us with periodic envelope, exponentially changeable soliton envelope, rational rogue wave, periodic rogue wave, combo periodic-soliton, and combo rational-soliton solutions, which are much interesting phenomena in nonlinear sciences. Thus the results disclose that the proposed technique is very effective and straight-forward, and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.     

Chemical and structural characterization of α-N-acetylgalactosaminidase I and II from starfish, <Emphasis Type="Italic">asterina amurensis</Emphasis>

Background

The marine invertebrate starfish was found to contain a novel α-N-acetylgalactosaminidase, α-GalNAcase II, which catalyzes removal of terminal α-N-acetylgalactosamine (α-GalNAc), in addition to a typical α-N-acetylgalactosaminidase, α-GalNAcase I, which catalyzes removal of terminal α-N-acetylgalactosamine (α-GalNAc) and, to a lesser extent, galactose. The interrelationship between α-GalNAcase I and α-GalNAcase II and the molecular basis of their differences in substrate specificity remain unknown.

Results

Chemical and structural comparisons between α-GalNAcase I and II using immunostaining, N-terminal amino acid sequencing and peptide analysis showed high homology to each other and also to other glycoside hydrolase family (GHF) 27 members. The amino acid sequence of peptides showed conserved residues at the active site as seen in typical α-GalNAcase. Some substitutions of conserved amino acid residues were found in α-GalNAcase II that were located near catalytic site. Among them G171 and A173, in place of C171 and W173, respectively in α-GalNAcase were identified to be responsible for lacking intrinsic α-galactosidase activity of α-GalNAcase II. Chemical modifications supported the presence of serine, aspartate and tryptophan as active site residues. Two tryptophan residues (W16 and W173) were involved in α-galactosidase activity, and one (W16) of them was involved in α-GalNAcase activity.

Conclusions

The results suggested that α-GalNAcase I and II are closely related with respect to primary and higher order structure and that their structural differences are responsible for difference in substrate specificities.

     

Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

Under inquisition in this paper is a $(2+1)$-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.