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Your search keyword '"Qiao, Zhijun"' showing total 746 results
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746 results on '"Qiao, Zhijun"'

1. Rogue peakon, well-posedness, ill-posedness and blow-up phenomenon for an integrable Camassa-Holm type equation

Author

Zhu, Mingxuan, Zeng, Zhenteng, Jiang, Zaihong, Xia, Baoqiang, and Qiao, Zhijun

Subjects
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, 37K10, 35G25, 35L05
Abstract

In this paper, we study an integrable Camassa-Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon) solution - called {\sf rogue peakon}, that is given in a rational form with some logarithmic function, but not a regular traveling wave. We also provide multi-rogue peakon solutions. Furthermore, we discuss the local well-posedness of the solution in the Besov space $B_{p,r}^{s}$ with $1\leq p,r\leq\infty$, $s>\max \left\{1+1/p,3/2\right\}$ or $B_{2,1}^{3/2}$, and then prove the ill-posedness of the solution in $B_{2,\infty}^{3/2}$. Moreover, we establish the global existence and blow-up phenomenon of the solution, which is, if $m_0(x)=u_0-u_{0xx}\geq(\not\equiv) 0$, then the corresponding solution exists globally, meanwhile, if $m_0(x)\leq(\not\equiv) 0$, then the corresponding solution blows up in a finite time., Comment: 23 pages, 6 figures

Published
2023

3. Pangenome analysis reveals genomic variations associated with domestication traits in broomcorn millet

Author

Chen, Jinfeng, Liu, Yang, Liu, Minxuan, Guo, Wenlei, Wang, Yongqiang, He, Qiang, Chen, Weiyao, Liao, Yi, Zhang, Wei, Gao, Yuanzhu, Dong, Kongjun, Ren, Ruiyu, Yang, Tianyu, Zhang, Liyuan, Qi, Mingyu, Li, Zhiguang, Zhao, Min, Wang, Haigang, Wang, Junjie, Qiao, Zhijun, Li, Haiquan, Jiang, Yanmiao, Liu, Guoqing, Song, Xiaoqiang, Deng, Yarui, Li, Hai, Yan, Feng, Dong, Yang, Li, Qingquan, Li, Tao, Yang, Wenyao, Cui, Jianghui, Wang, Hongru, Zhou, Yongfeng, Zhang, Xiaoming, Jia, Guanqing, Lu, Ping, Zhi, Hui, Tang, Sha, and Diao, Xianmin

Published
2023
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10. A graph-based genome and pan-genome variation of the model plant Setaria

Author

He, Qiang, Tang, Sha, Zhi, Hui, Chen, Jinfeng, Zhang, Jun, Liang, Hongkai, Alam, Ornob, Li, Hongbo, Zhang, Hui, Xing, Lihe, Li, Xukai, Zhang, Wei, Wang, Hailong, Shi, Junpeng, Du, Huilong, Wu, Hongpo, Wang, Liwei, Yang, Ping, Xing, Lu, Yan, Hongshan, Song, Zhongqiang, Liu, Jinrong, Wang, Haigang, Tian, Xiang, Qiao, Zhijun, Feng, Guojun, Guo, Ruifeng, Zhu, Wenjuan, Ren, Yuemei, Hao, Hongbo, Li, Mingzhe, Zhang, Aiying, Guo, Erhu, Yan, Feng, Li, Qingquan, Liu, Yanli, Tian, Bohong, Zhao, Xiaoqin, Jia, Ruiling, Feng, Baili, Zhang, Jiewei, Wei, Jianhua, Lai, Jinsheng, Jia, Guanqing, Purugganan, Michael, and Diao, Xianmin

Published
2023
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11. Pseudo-peakons and Cauchy analysis for an integrable fifth-order equation of Camassa-Holm type

Author

Reyes, Enrique G., Zhu, Mingxuan, and Qiao, Zhijun

Subjects
Mathematics - Analysis of PDEs, Nonlinear Sciences - Exactly Solvable and Integrable Systems
Abstract

In this paper we discuss integrable higher order equations {\em of Camassa-Holm (CH) type}. Our higher order CH-type equations are "geometrically integrable", that is, they describe one-parametric families of pseudo-spherical surfaces, in a sense explained in Section 1, and they are integrable in the sense of zero curvature formulation ($\simeq$ Lax pair) with infinitely many local conservation laws. The major focus of the present paper is on a specific fifth order CH-type equation admitting {\em pseudo-peakons} solutions, that is, weak bounded solutions with differentiable first derivative and continuous and bounded second derivative, but such that any higher order derivative blows up. Furthermore, we investigate the Cauchy problem of this fifth order CH-type equation on the real line and prove local well-posedness under the initial conditions $u_0 \in H^s(\mathbb{R})$, $s > 7/2$. In addition, we study conditions for global well-posedness in $H^4(\mathbb{R})$ as well as conditions causing local solutions to blow up in a finite time. We conclude our paper with some comments on the geometric content of the high order CH-type equations., Comment: 6 figures; 32 pages

Published
2021

21. Local well-posedness and blow-up for a family of $U(1)$-invariant peakon equations

Author

Anco, Stephen C., He, Huijun, and Qiao, Zhijun

Subjects
Mathematics - Analysis of PDEs, Mathematical Physics
Abstract

The Cauchy problem for a unified family of integrable $U(1)$-invariant peakon equations from the NLS hierarchy is studied. As main results, local well-posedness is proved in Besov spaces, and blow-up is established through use of an $L^1$ conservation law., Comment: 29 pages

Published
2020

22. Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space

Author

Zhang, Lei and Qiao, Zhijun

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space $B_{2,1}^{\frac{1}{2}}(\mathbb{T})$. Our results shows that in comparison with the well-known work for classic Camassa-Holm-type equations, the existence of global solution only relies on the $L^1$-integrability of the variable coefficients $\alpha(t)$ and $\gamma(t)$, but nothing to do with the shape or smoothness of the initial data. The key ingredient of the proof hinges on the careful analysis of the mutual effect among two component forms, the uniform bound of approximate solutions, and several crucial estimates of cubic nonlinearities in low-regularity Besov spaces via the Littlewood-Paley decomposition theory. A reduced case in our results yields the global existence of solutions in a Besov space for two kinds of well-known isospectral peakon system with weakly dissipative terms.} Moreover, we derive two kinds of precise blow-up criteria for a strong solution in both critical and non-critical Besov spaces, as well as providing specific characterization for the lower bound of the blow-up time, which implies the global existence with additional conditions on the time-dependent parameters $\alpha(t)$ an $\gamma(t)$.

Published
2020

38. On the Cauchy problem for a higher-order $\mu$-Camassa-Holm equation

Author

Wang, Feng, Li, Fengquan, and Qiao, Zhijun

Subjects
Mathematical Physics, 35G25, 35L05, 35B30
Abstract

In this paper, we study the Cauchy problem of a higher-order $\mu$-Camassa-Holm equation. We first establish the Green's function of $(\mu-\partial_{x}^{2}+\partial_{x}^{4})^{-1}$ and local well-posedness for the equation in Sobolev spaces $H^{s}(\mathbb{S})$, $s>\frac{7}{2}$. Then we provide the global existence results for strong solutions and weak solutions. Moreover, we show that the solution map is non-uniformly continuous in $H^{s}(\mathbb{S})$, $s\geq 4$. Finally, we prove that the equation admits single peakon solutions., Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1712.07996

Published
2017

39. Well-posedness and peakons for a higher-order $\mu$-Camassa-Holm equation

Author

Wang, Feng, Li, Fengquan, and Qiao, Zhijun

Subjects
Mathematical Physics, 35G25, 35L05, 35B30
Abstract

In this paper, we study the Cauchy problem of a higher-order $\mu$-Camassa-Holm equation. By employing the Green's function of $(\mu-\partial_{x}^{2})^{-2}$, we obtain the explicit formula of the inverse function $(\mu-\partial_{x}^{2})^{-2}w$ and local well-posedness for the equation in Sobolev spaces $H^{s}(\mathbb{S})$, $s>\frac{7}{2}$. Then we prove the existence of global strong solutions and weak solutions. Moreover, we show that the data-to-solution map is H\"{o}lder continuous in $H^{s}(\mathbb{S})$, $s\geq 4$, equipped with the $H^{r}(\mathbb{S})$-topology for $0\leq r

Published
2017

47. Alice-Bob Peakon Systems

Author

Lou, Senyue and Qiao, Zhijun

Subjects
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Abstract

In this letter, we study the Alice-Bob peakon system generated from an integrable peakon system through using the strategy of the so-called Alice-Bob non-local KdV approach [13]. Non-local integrable peakon equations are obtained and shown to have peakon solutions., Comment: 3 figures

Published
2017
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48. Effects of Rehydration on Bacterial Diversity in the Rhizosphere of Broomcorn Millet (Panicum miliaceum L.) after Drought Stress at the Flowering Stage.

Author

Liu, Yuhan, Mao, Jiao, Xu, Yuanmeng, Ren, Jiangling, Wang, Mengyao, Wang, Shu, Liu, Sichen, Wang, Ruiyun, Wang, Lun, Wang, Liwei, Qiao, Zhijun, and Cao, Xiaoning

Subjects
BROOMCORN millet, BACTERIAL diversity, MICROBIAL diversity, RHIZOBACTERIA, DROUGHT tolerance
Abstract

This study aimed to elucidate responses of the bacterial structure and diversity of the rhizosphere in flowering broomcorn millet after rehydration following drought stress. In this study, the broomcorn millet varieties 'Hequ red millet' (A1) and 'Yanshu No.10′ (A2), known for their different drought tolerance levels, were selected as experimental materials. The plants were subjected to rehydration after drought stress at the flowering stage, while normal watering (A1CK and A2CK) served as the control. Soil samples were collected at 10 days (A11, A21, A1CK1, and A2CK1) and 20 days (A12, A22, A1CK2, and A2CK2) after rehydration. High-throughput sequencing technology was employed to investigate the variations in bacterial community structure, diversity, and metabolic functions in the rhizosphere of the broomcorn millet at different time points following rehydration. The findings indicated that the operational taxonomic units (OTUs) of bacteria in the rhizosphere of broomcorn millet were notably influenced by the duration of treatment, with a significant decrease in OTUs observed after 20 days of rehydration. However, bacterial Alpha diversity was not significantly impacted by rehydration following drought stress. The bacterial community in the rhizosphere of broomcorn millet was mainly composed of Actinobacteria and Proteobacteria. After rewatering for 10 to 20 days after drought stress, the abundance of Sphingomonas and Aeromicrobium in the rhizosphere soil of the two varieties of broomcorn millet decreased gradually. Compared with Yanshu No.10, the abundance of Pseudarthrobacter in the rhizosphere of Hequ red millet gradually increased. A Beta diversity analysis revealed variations in the dissimilarities of the bacterial community which corresponded to different rehydration durations. The relative abundance of bacterial metabolic functions in the rhizosphere of broomcorn millet was lower after 20 days of rehydration, compared to measurements after 10 days of rehydration. This observation might be attributed to the exchange of materials between broomcorn millet and microorganisms during the initial rehydration stage to repair the effects of drought, as well as to the enrichment of numerous microorganisms to sustain the stability of the community structure. This study helps to comprehend the alterations to the bacterial structure and diversity in the rhizosphere of broomcorn millet following drought stress and rehydration. It sheds light on the growth status of broomcorn millet and its rhizosphere microorganisms under real environmental influences, thereby enhancing research on the drought tolerance mechanisms of broomcorn millet. [ABSTRACT FROM AUTHOR]

Published
2024
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49. Effect of Different Fertilizer Types on Quality of Foxtail Millet under Low Nitrogen Conditions.

Author

Zheng, Tingting, Wang, Shu, Wang, Mengyao, Mao, Jiao, Xu, Yuanmeng, Ren, Jiangling, Liu, Yuhan, Liu, Sichen, Qiao, Zhijun, and Cao, Xiaoning

Subjects
PHOSPHATE fertilizers, NITROGEN fertilizers, ORGANIC fertilizers, FOXTAIL millet, PHOSPHORUS compounds, NITROGEN compounds
Abstract

In order to clarify the effect of different fertilizers on foxtail millet quality under low nitrogen conditions, we used JGNo.21 and LZGNo.2 as experimental materials and set up five treatments, including non-fertilization, nitrogen, phosphorus, compound, and organic fertilizers, to study the regulation of different fertilizer types on agronomic traits, nutrient fractions, and pasting characteristics of foxtail millet under low nitrogen conditions. Compared with the control, all of the fertilizers improved the agronomic traits of JGNo.21 to a certain extent. Nitrogen and compound fertilizer treatments reduced the starch content of JGNo.21; the starch content was reduced by 0.55% and 0.07% under nitrogen and compound fertilizers treatments. Phosphorus and organic fertilizers increased starch content, and starch content increased by 0.50% and 0.56% under phosphorus and organic fertilizer treatments. The effect of each fertilizer treatment on protein content was completely opposite to that of starch; different fertilizer treatments reduced the fat content of JGNo.21 and increased the fiber content. Among them, nitrogen and phosphorus fertilizers increased the yellow pigment content; the yellow pigment content increased by 1.21% and 2.64% under nitrogen and phosphorus fertilizer treatments. Organic and compound fertilizers reduced the content of yellow pigment; the yellow pigment content was reduced by 3.36% and 2.79% under organic and compound fertilizer treatments. Nitrogen and organic fertilizers increased the fat content of LZGNo.2; the fat content increased by 2.62% and 1.98% under nitrogen, organic fertilizer treatment. Compound and phosphorus fertilizer decreased the fat content; the fat content decreased by 2.16% and 2.90% under compound and phosphorus fertilizer treatment. Different fertilizer treatments reduced the cellulose and yellow pigment content of LZGNo.2. The content of essential, non-essential, and total amino acids of JGNo.21 was increased under compound and nitrogen fertilizer treatments and decreased under organic and phosphorus fertilizer treatments. The content of essential, non-essential, and total amino acids of LZGNo.2 was significantly higher under compound, nitrogen, and organic fertilizer treatments compared with control and significantly decreased under phosphorus fertilizer treatments. Nitrogen and compound fertilizer treatments significantly reduced the values of peak viscosity, trough viscosity, breakdown viscosity, final viscosity, setback viscosity, and pasting time of each index of JGNo.21; phosphorus and organic fertilizer treatments improved the values of each index. In contrast, the pasting viscosity of LZGNo.2 increased under phosphorus fertilizer treatment and decreased under nitrogen fertilizer treatment. Reasonable fertilization can improve the quality of foxtail millet, which provides a scientific theoretical basis for improving the quality of foxtail millet. [ABSTRACT FROM AUTHOR]

Published
2024
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