Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrodinger system in an inhomogeneous optical fiber

Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.

一个特殊集类上测度的扩张

定义了一个新集类L-弱半环,并借助给出的外测度的等价定义得到其上的测度扩张定理,该定理是对Carathéodory测度扩张定理的一种推广.

High-order breather,M-kink lump and semi-rational solutions of potential Kadomtsev-Petviashvili equation

N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev-Petviashvili equation are derived by means of the Hirota bilinear method,and the limit process of high-order synchronized breathers are shown.Furthermore,M-lump solutions are also presented by taking the long wave limit.Additionally,a family of semi-rational solutions with elastic collision are generated by taking a long-wave limit of only a part of exponential functions,their interaction behaviors are shown by three-dimensional plots and contour plots.

Vector semi-rational rogon-solitons and asymptotic analysis for any multi-component Hirota equations with mixed backgrounds

The Hirota equation can be used to describe the wave propagation of an ultrashort optical field.In this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with mixed non-zero and zero boundary conditions are explored.We employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions(i.e.nonlinear combinations of rogon and soliton solutions).The semi-rational rogon-soliton features can be modulated by the polynomial degree.For the larger solution parameters,the first m(m<n)components with non-zero backgrounds can be decomposed into rational rogons and grey-like solitons,and the last n-m components with zero backgrounds can approach bright-like solitons.Moreover,we analyze the accelerations and curvatures of the quasi-characteristic curves,as well as the variations of accelerations with the distances to judge the interaction intensities between rogons and grey-like solitons.We also find the semi-rational rogon-soliton solutions with ultrahigh amplitudes.In particular,we can also deduce vector semi-rational solitons of the ncomponent complex mKdV equation.These results will be useful to further study the related nonlinear wave phenomena of multi-component physical models with mixed background,and even design the related physical experiments.

Modification of the substrate specificity of leucine dehydrogenase by site‑directed mutagenesis based on biocomputing strategies

Synthesis of chiral amines by amine dehydrogenase has the advantages of environmental friendliness,high stereoselectivity,and mild reaction conditions.However,amine dehydrogenase has low catalytic activity,which greatly limits its application in the large-scale synthesis of chiral amines.In this study,a novel amine dehydrogenase was obtained by modifying the substrate specificity of leucine dehydrogenase via computer-aided protein engineering strategy.Furthermore,conservation analysis,homology modeling and molecular docking analysis were carried out via biocomputing strategy to select the mutation sites,and the mutants L52S and T143C were obtained.The enzyme activities of the two mutants to 2-pentanone were 1.55 U/mg and 2.06 U/mg,respectively.The enzyme activity of the latter was 188%and the Tm value was 2.55°Chigher than those of the original mutant,which laid a foundation for the efficient preparation of chiral amines by using this novel enzyme.

Structure-guided protein design of fluoroacetate dehalogenase for kinetic resolution of rac-2-bromobutyric acid

R-2-Bromobutyric acid is a very important intermediate for the synthesis of agrochemicals and pharmaceuticals.Bioresolution of rac-2-bromobutyric acid(rac-2-BBA)provides a promising process for R-2-bromobutyric acid(R-2-BBA)production.The fluoroacetate dehalogenase(FAcD)has been always studied in the defluorination process.We found that FAcD RPA1163 showed detectable activity but no enantioselectivity towards rac-2-BBA.The iterative saturation mutagenesis(ISM)of FAcD RPA1163 resulted in a mutant H155V/W156R/Y219M,which catalyzed the kinetic resolution of rac-2-BBA to produce R-2-BBA with enhanced activity and enantioselectivity(99.3%ee).The high preference for S-2-bromobutyric acid(S-2-BBA)is of synthetic value.Molecular docking analysis indicated that the H155V/W156R/Y219M mutation reduced steric hindrance and broadened the halide pocket.It is not only the steric hindrance but also the electrostatic environment that has an effect on the activity and enantioselectivity.