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This paper explores the Konopelchenko–Dubrovsky (KD) equation and employs Hirota's bilinear method and Kadomtsev–Petviashvili (KP) hierarchy reduction technique to construct solitons, line breathers, rational solutions, and algebraic solitons within the system. These solutions are represented using N × N determinants. When the determinant size N is odd, periodic background solutions are generated, while even N values yield solutions on constant backgrounds. By utilizing asymptotic analysis, the paper elucidates explicit expressions for asymptotic algebraic solitons localized in a straight line for the algebraic soliton solutions. The dynamics of the obtained solutions are further examined and illustrated through plots. [ABSTRACT FROM AUTHOR]

The characteristics of the runoff and sediment in the Yellow River were analysed and predicted Based on measured data of from 1951 to 2017. Initially, the phase characteristics of runoff and sediment were analysed by the cumulative anomaly curve method. After that, the trend and catastrophe of runoff and sediment are discuessed using the Mann-Kendall methods. The results revealed that the decreasing trend of runoff and sediment was significant, and the catastrophe time was 1979 and 1992, respectively. Finally, the evolution of the runoff and sediment was predicted quantitatively by using the ARMA model. The predictions indicated that, the Yellow River is likely to remain in the stage of low runoff and sediment. [ABSTRACT FROM AUTHOR]

This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ⩾ 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem. [ABSTRACT FROM AUTHOR]

The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, priori estimates for the solution was given. At last, the existence of the weak solution of MKdV-Burgers equation was proved and the global-exponential and asymptotic stability of the solution of MKdV-Burgers equation was given. [ABSTRACT FROM AUTHOR]

This work aimed to discuss the effects of exogenous abscisic acid (ABA) on the root growth regulation of maize seedlings under chilling stress. The roots of the maize cultivar Zhengdan 958 were irrigated with ABA (10−7, 10−6, 10−5 and 10−4 M) at the third true leaf stage under chilling duration (0, 2, 4, 6, and 8 days). The biomass, the phenylalanine ammonia lyase (PAL), and polyphenol oxidase (PPO) enzyme activities, total phenolic and flavonoid contents, the ferric reducing ability of plasma (FRAP) antioxidant capacity, and 2,2-azinobis (3-ethlbenzothiazo-line-6-sulfonic acid) diammonium salt radical (ABTS·+) scavenging capacity of the roots of maize seedlings were measured after the treatment. The results showed that appropriate concentrations of exogenous ABA effectively enhanced root biomass, increased PAL and PPO enzyme activities, and significantly increased total phenolic contents and flavonoid contents. Moreover, the ABA markedly improved the FRAP antioxidant capacity and ABTS·+ scavenging capacity under low-temperature stress. These results indicate that ABA-treated maize seedlings are resistant to chilling stress and that the optimum concentration of ABA is 10−5 M. Exogenous applications of ABA have a concentration effect in alleviating chilling stress, in which low concentrations have a promoting effect and high concentrations have an inhibiting effect. [ABSTRACT FROM AUTHOR]