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Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions

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Communications in Theoretical Physics 2024年第1期76卷 1-6页

作者： Engui Fan Yanxi Zhang School of Mathematical sciences and Key laboratory of mathematics for nonlinear science Fudan UniversityShanghai200433China Tianjin Xinhua High School No.99 machang RoadTianjin300204China

In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS *** the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.

关键词： defocusing Kundu-Eckhaus equation Riemann-Hilbert problems steepest descent method soliton resolution asymptotic stability Painleve transcendents

Q-homotopy analysis method for time-fractional Newell–Whitehead equation and time-fractional generalized Hirota–Satsuma coupled KdV system

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Communications in Theoretical Physics 2024年第3期76卷 70-83页

作者： Di Liu Qiongya Gu Lizhen Wang Center for nonlinear Studies School of MathematicsNorthwest UniversityXi'an710127China

In this paper,two types of fractional nonlinear equations in Caputo sense,time-fractional Newell–Whitehead equation(FNWE)and time-fractional generalized Hirota–Satsuma coupled KdV system(HS-cKdVS),are investigated by means of the q-homotopy analysis method(q-HAM).The approximate solutions of the proposed equations are constructed in the form of a convergent series and are compared with the corresponding exact *** to the presence of the auxiliary parameter h in this method,just a few terms of the series solution are required in order to obtain better *** the sake of visualization,the numerical results obtained in this paper are graphically displayed with the help of Maple.

关键词： fractional Newell-Whitehead equation fractional generalized Hirota-Satsuma coupled KdV system approximate solution q-homotopy analysis method

Time-dependent Global Attractors for the Nonclassical Diffusion Equations with Fading Memory

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Acta Mathematicae Applicatae Sinica 2024年

作者： Yu-ming QIN Xiao-ling CHEN Department of mathematics Donghua University Department of mathematics Institute for Nonlinear Science Donghua University

In this paper, we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term f satisfies critical exponential growth and the external force g(x)∈L2(Ω). In the framework of time-dependent spaces, we verify the existence of absorbing sets and the asymptotic compactness of the process, then we obtain the existence of the time-dependent global attractor A={At}t∈Rin Mt. Furthermore, we achieve the regularity of A, that is, Atis bounded in Mt1with a bound independent of t.

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Prediction of chemical short-range order in high-/medium-entropy alloys

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Journal of Materials science & Technology 2024年第2期169卷 115-123页

作者： Pei-Yu Cao Jing Wang Ping Jiang Yun-Jiang Wang Fu-Ping Yuan Xiao-Lei Wu State Key laboratory of nonlinear Mechanics Institute of MechanicsChinese Academy of ScienceBeijing 100190China School of Engineering science University of Chinese Academy of SciencesBeijing 100049China

Chemical short-range orders(CSROs),as the built-in sub-nanoscale entities in a high-/medium-entropy alloy(H/MEA),have aroused an ever-increasing *** multi-principal elements in an H/MEA to form a complex concentrated solution,a variety of sub-systems of species exist to induce the metastable ordered compounds as candidates for ultimate *** issues remain pending on the origin of CSROs as to how to judge if CSRO will form in an H/MEA and particularly,what kind of CSROs would be stably produced if there were multiple ***,the first-principles method,along with the proposed local formation energy calculation in allusion to the atomic-scale chemical heterogeneities,is used to predict the CSRO formation based on the mechanical stability,thermodynamic formation energy,and electronic *** simulations are detailed in an equiatomic ternary VCoNi MEA with three kinds of potential compounds,i.e.,L1_(1),L1_(2),and B2,in the face-centered cubic *** turns out that L1_(1)is stable but hard to grow up so as to become the final CSRO.L1_(1)is further predicted as CSROs in CrCoNi,but unable to form in FeCoNi and CrMnFeCoNi *** predictions are consistent with the experimental *** findings shed light on understanding the formation of *** method is applicable to other H/MEAs to design and tailor CSROs by tuning chemical species/contents and thermal processing for high performance.

关键词： Short-range order High-entropy alloy Microstructure First-principles calculation Gibbs free energy Local electronic density of states

Long-time asymptotic behavior for the nonlocal nonlinear Schro¨dinger equation in the solitonic region

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science China mathematics 2024年

作者： Gaozhan Li Yiling Yang Engui Fan School of Mathematical sciences and Key laboratory of mathematics for nonlinear sciences Fudan University

In this paper, we extend the ■-steepest descent method to study the Cauchy problem for the nonlocal nonlinear Schr?dinger（NNLS） equation with weighted Sobolev initial data iqt+qxx+2σ■2（x, t）q（-x, t） = 0,q（x, 0） = q0（x）,where q0∈ H1,1（R）. Based on the spectral analysis of the Lax pair, the solution of the Cauchy problem is expressed in terms of the solution of a Riemann-Hilbert problem, which is transformed into a solvable model after a series of deformations. We further obtain the asymptotic expansion of the solution to the Cauchy problem for the NNLS equation in the solitonic region. The leading term is soliton solutions, the second term is the interaction between solitons and dispersion, and the error term comes from a corresponding?ˉ-*** with the asymptotic results on the classical NLS equation, the major difference is the second and third terms of the asymptotic expansion for the NNLS equation, which were affected by a function depending on the scattering data and the stationary phase point.

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Discontinuous phase diagram of amorphous carbons

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National science Review 2024年第4期11卷 164-171页

作者： YinBo Zhu ZhouYu Fang ZhongTing Zhang HengAn Wu CAS Key laboratory of Mechanical Behavior and Design of Materials Department of Modern MechanicsUniversity of Science and Technology of China State Key laboratory of nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences

The short-range order and medium-range order of amorphous carbons demonstrated in experiments allow us to rethink whether there exist intrinsic properties hidden by atomic disordering. Here we presented six representative phases of amorphous carbons（0.1–3.4 g/cm3）, namely, disordered graphene network（DGN）, high-density amorphous carbon（HDAC）, amorphous diaphite（a-DG）, amorphous diamond（a-D）, paracrystalline diamond（p-D）, and nano-polycrystalline diamond（NPD）, respectively, classified by their topological features and microstructural characterizations that are comparable with experiments. To achieve a comprehensive physical landscape for amorphous carbons, a phase diagram was plotted in the sp3/sp2versus density plane, in which the counterintuitive discontinuity originates from the inherent difference in topological microstructures, further guiding us to discover a variety of phase transitions among different amorphous carbons. Intriguingly, the power law, log（sp3/sp2） ∝ ρn, hints at intrinsic topology and hidden order in amorphous carbons, providing an insightful perspective to reacquaint atomic disorder in non-crystalline carbons.

关键词： amorphous carbons disordered carbons phase diagram microstructural topology phase transition

On fractional discrete financial system:Bifurcation,chaos,and control

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Chinese Physics B 2024年第10期33卷 129-140页

作者： Louiza Diabi Adel Ouannas Amel Hioual Shaher Momani Abderrahmane Abbes laboratory of Dynamical Systems and Control University of Larbi Ben M’hidiOum El Bouaghi 04000Algeria Department of mathematics and Computer science University of Larbi Ben M’hidiOum El Bouaghi 04000Algeria nonlinear Dynamics Research Center Ajman UniversityAjman 346United Arab Emirates Department of mathematics The University of JordanAmman 11942Jordan laboratory of mathematics Dynamics and ModelizationUniversity Badji MokhtarAnnaba 23000Algeria

The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial *** paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate *** such,we evaluate when the equilibrium points are stable or unstable at various fractional *** use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov *** techniques reveal that financial maps exhibit chaotic attractor *** study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate ***,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy ***,we offer nonlinear-type controllers to stabilize the fractional financial *** numerical results of this study are obtained using MATLAB.

关键词： financial model stability chaos commensurate and incommensurate orders complexity

Elastic wave insulation and propagation control based on the programmable curved-beam periodic structure

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Applied mathematics and Mechanics(English Edition) 2024年第10期45卷 1791-1806页

作者： Jiajia MAO Hong CHENG Tianxue MA Beijing Key laboratory of nonlinear Vibrations and Strength of Mechanical Structures Department of MechanicsSchool of MathematicsStatistics and MechanicsBeijing University of TechnologyBeijing 100124China Department of Mechanics School of Physical Science and EngineeringBeijing Jiaotong UniversityBeijing 100044China

Curved-beams can be used to design modular multistable metamaterials(MMMs)with reprogrammable material properties,i.e.,programmable curved-beam periodic structure(PCBPS),which is promising for controlling the elastic wave *** PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap,analyze the wave propagation mechanisms,and further form its geometrical and physical criteria for tuning the elastic wave *** the equivalent model,we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability,and investigate the wave propagation characteristics through the *** validate the equivalent system,the finite element method(FEM)is *** is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical *** findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control.

关键词： curved-beam based periodic structure equivalent stiffness spring-oscillator system dispersion relation wave propagation

A vibration isolator with a controllable quasi-zero stiffness region based on nonlinear force design

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Applied mathematics and Mechanics(English Edition) 2024年第8期45卷 1279-1294页

作者： Xinyu LIAN Bing LIU Huaxia DENG Xinglong GONG CAS Key laboratory of Mechanical Behavior and Design of Materials Department of Modern MechanicsUniversity of Science and Technology of ChinaHefei 230027China State Key laboratory of nonlinear Mechanics Institute of MechanicsChinese Academy of SciencesBeijing 100190China State Key laboratory of Fire science University of Science and Technology of ChinaHefei 230026China

To achieve stability optimization in low-frequency vibration control for precision instruments,this paper presents a quasi-zero stiffness(QZS)vibration isolator with adjustable nonlinear ***,the stress-magnetism coupling model is established through meticulous theoretical *** controllable QZS interval is constructed via parameter design and magnetic control,effectively segregating the high static stiffness bearing section from the QZS vibration isolation ***,a displacement control scheme utilizing a magnetic force is proposed to regulate entry into the QZS working range for the vibration isolation *** results demonstrate that the operation within this QZS region reduces the peak-to-peak acceleration signal by approximately 66.7%compared with the operation outside this region,thereby significantly improving the low frequency performance of the QZS vibration isolator.

关键词： low frequency nonlinear vibration isolator quasi-zero stiffness(QzS)