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Traveling Wave Solutions of a SIR Epidemic Model with Spatio-Temporal Delay
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作者 Zhihe Hou 《Journal of Applied Mathematics and Physics》 2024年第10期3422-3438,共17页
In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of t... In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution. 展开更多
关键词 Susceptible-Infected-Recovered Epidemic Model traveling Wave solutions Spatio-Temporal Delay Schauder Fixed Point Theorem
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Stability of Traveling Waves Solutions for Nonlinear Cellular Neural Networks with Distributed Delays
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作者 GUO Yingxin GE Shuzhi Sam ARBI Adnène 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2022年第1期18-31,共14页
This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks.As a continuity of the past work(Wu and Niu,2016;Yu,et al.,2011)on the existence and uniquen... This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks.As a continuity of the past work(Wu and Niu,2016;Yu,et al.,2011)on the existence and uniqueness of the traveling wave solutions,it is very reasonable and interesting to consider the exponential stability of the traveling wave solutions.By the weighted energy method,comparison principle and the first integral mean value theorem,this paper proves that,for all monotone traveling waves with the wave speed c<c1*<0 or c>c2*>0,the solutions converge time-exponentially to the corresponding traveling waves,when the initial perturbations decay at some fields. 展开更多
关键词 Cellular delayed neural networks comparison principle stability analysis traveling waves solutions
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Parameter Identification in Traveling Wave Solutions of a Modified Fisher’s Equation
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作者 Zhixuan Jia Ali Nadim 《Applied Mathematics》 2023年第5期290-313,共24页
In this work, we focus on the inverse problem of determining the parameters in a partial differential equation from given numerical solutions. For this purpose, we consider a modified Fisher’s equation that includes ... In this work, we focus on the inverse problem of determining the parameters in a partial differential equation from given numerical solutions. For this purpose, we consider a modified Fisher’s equation that includes a relaxation time in relating the flux to the gradient of the density and an added cubic non-linearity. We show that such equations still possess traveling wave solutions by using standard methods for nonlinear dynamical systems in which fixed points in the phase plane are found and their stability characteristics are classified. A heteroclinic orbit in the phase plane connecting a saddle point to a node represents the traveling wave solution. We then design parameter estimation/discovery algorithms for this system including a few based on machine learning methods and compare their performance. 展开更多
关键词 PDE traveling Wave Solution Stability Analysis Machine Learning Optimization EMBEDDING
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Exact Traveling Wave Solutions of the Generalized Fractional Differential mBBM Equation
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作者 Yuting Zhong Renzhi Lu Heng Su 《Advances in Pure Mathematics》 2023年第3期167-173,共7页
By using the fractional complex transform and the bifurcation theory to the generalized fractional differential mBBM equation, we first transform this fractional equation into a plane dynamic system, and then find its... By using the fractional complex transform and the bifurcation theory to the generalized fractional differential mBBM equation, we first transform this fractional equation into a plane dynamic system, and then find its equilibrium points and first integral. Based on this, the phase portraits of the corresponding plane dynamic system are given. According to the phase diagram characteristics of the dynamic system, the periodic solution corresponds to the limit cycle or periodic closed orbit. Therefore, according to the phase portraits and the properties of elliptic functions, we obtain exact explicit parametric expressions of smooth periodic wave solutions. This method can also be applied to other fractional equations. 展开更多
关键词 A Generalized Fractional Differential mBBM Equation traveling Wave Solution Phase Portrait
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All Single Traveling Wave Solutions to (3+1)-Dimensional Nizhnok-Novikov-Veselov Equation 被引量:12
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作者 LIU Cheng-Shi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第6期991-992,共2页
Using elementary integral method, a complete classification of all possible exact traveling wave solutions to (3+1)-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
关键词 (3+1)-dimensional Nizhnok-Novikov-Veselov equation traveling wave solution elementary integral method
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Representations and Classification of Traveling Wave Solutions to sinh-Grdon Equation 被引量:4
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作者 LIU Cheng-Shi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第1期153-158,共6页
Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are di... Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. (Beijing, China) 45 (2006) 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions. 展开更多
关键词 traveling wave solution atom solution exact solution sinh-GSrdon equation elliptic function
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EXACT TRAVELING WAVE SOLUTIONS OF MODIFIED ZAKHAROV EQUATIONS FOR PLASMAS WITH A QUANTUM CORRECTION 被引量:4
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作者 房少梅 郭昌洪 郭柏灵 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期1073-1082,共10页
In this article, the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method, hyperbolic secant expansion m... In this article, the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method, hyperbolic secant expansion method, and Jacobi elliptic function ex- pansion method. They obtain more exact traveling wave solutions including trigonometric function solutions, rational function solutions, and more generally solitary waves, which are called classical bright soliton, W-shaped soliton, and M-shaped soliton. 展开更多
关键词 Modified Zakharov equations Quantum correction Exact traveling wave solution Function expansion method M-shaped soliton
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Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation 被引量:3
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作者 Ming Song Beidan Wang Jun Cao 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第10期148-153,共6页
We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane ... We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation. 展开更多
关键词 bifurcation theory generalized modified dispersive water wave equation traveling wave solution
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ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM 被引量:2
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作者 蒋咪娜 向建林 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1325-1338,共14页
This paper is concerned with the existence and the nonlinear asymptotic stabil- ity of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations {θt=vζx+(ζθ)x+aθxx,ζt=-θ... This paper is concerned with the existence and the nonlinear asymptotic stabil- ity of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations {θt=vζx+(ζθ)x+aθxx,ζt=-θx+βζxx;with initial data and end states (ζθ)(x,0)=(ζ0,θ0)(x)→(ζ±,θ±)as x→∞.We obtain the existence of traveling wave solutions by phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without restrictions on the coeffi- cients a and v by the method of energy estimates. 展开更多
关键词 dissipative evolution equations traveling wave solutions nonlinear stability energy estimates
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New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation 被引量:2
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作者 Zhiyun Zeng Xiaohua Liu +1 位作者 Yin Zhu Xue Huang 《Journal of Applied Mathematics and Physics》 2022年第2期333-346,共14页
In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the co... In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions. 展开更多
关键词 Exact traveling Wave solutions (2 + 1)-Dimensional Time-Fractional Zoomeron Equation The New Mapping Approach The New Extended Auxiliary Equation Approach
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Exact Traveling Wave Solutions for Generalized Camassa-Holm Equation by Polynomial Expansion Methods 被引量:1
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作者 Junliang Lu Xiaochun Hong 《Applied Mathematics》 2016年第14期1599-1611,共13页
We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the gener... We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the generalized Camassa-Holm Equation: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At the same time, we have shown graphical behavior of the traveling wave solutions. 展开更多
关键词 Camassa-Holm Equation Partial Differential Equation Polynomial Expansion Methods traveling Wave solutions
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Traveling Wave Solutions of the Incompressible Ideal Hall Magnetohydrodynamics
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作者 吴启鑫 夏振伟 杨维纮 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第6期71-73,共3页
The solutions of incompressible ideal Hall magnetohydrodynamics are obtained by using the traveling wave method. It is shown that the velocity and magnetic field parallel to the wave vector can be arbitrary constants.... The solutions of incompressible ideal Hall magnetohydrodynamics are obtained by using the traveling wave method. It is shown that the velocity and magnetic field parallel to the wave vector can be arbitrary constants. The velocity and magnetic field perpendicular to the wave vector are both helical waves. Moreover, the amplitude of the velocity perpendicular to the wave vector is related to the wave number and the circular frequency. In addition, further studies indicate that, no matter whether the uniform ambient magnetic field exists or not, the forms of the travelling wave solutions do not change. 展开更多
关键词 HALL et on is traveling Wave solutions of the Incompressible Ideal Hall Magnetohydrodynamics of MHD
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BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT
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作者 张卫国 刘强 +1 位作者 李正明 李想 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期941-959,共19页
This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solution... This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r^* which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if |r|≥ r^*; while they appear as damped oscillatory waves if |r| 〈 r^*. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u(ξ) in the global phase portraits, and then obtain the approximate solutions (u(ξ), H(ξ)). Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions. 展开更多
关键词 Variant Boussinesq equation with dissipation term shape analysis bounded traveling wave solution error estimate dissipation effect
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Dynamical behavior of traveling wave solutions of ion acoustic plasma equations
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作者 李庶民 贺天兰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第1期119-124,共6页
By using the theory of planar dynamical systems to the ion acoustic plasma equations, we obtain the existence of the solutions of the smooth and non-smooth solitary waves and the uncountably infinite smooth and non-sm... By using the theory of planar dynamical systems to the ion acoustic plasma equations, we obtain the existence of the solutions of the smooth and non-smooth solitary waves and the uncountably infinite smooth and non-smooth periodic waves. Under the given parametric conditions, we present the sufficient conditions to guarantee the existence of the above solutions. 展开更多
关键词 solitary traveling wave solution periodic traveling wave solution smoothness of waves ion acoustic plasma equations
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Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order
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作者 冯青华 孟凡伟 张耀明 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第12期17-25,共9页
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bo... In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. 展开更多
关键词 first integral method Riccati equation nonlinear equation traveling wave solution
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Some New Exact Traveling Wave Solutions of Double-sine-Gordon Equation
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作者 ZHENG Qiang REN Zhong-Zhou 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期303-304,共2页
The double-sine-Gordon equation is studied by means of the so-called mapping method. Some new exact solutions are determined.
关键词 double-sine-Gordon equation mapping method traveling wave solutions
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Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrodinger dynamical model and its applications
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作者 Xiaoyong Qian Dianchen Lu +1 位作者 Muhammad Arshad Khurrem Shehzad 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第2期154-163,共10页
We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),sol... We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),solitary waves,periodic and other wave solutions of the perturbed Kaup-Newell Schrodinger equation in mathematical physics are achieved by utilizing two mathematical techniques,namely,the extended F-expansion technique and the proposed exp(-φ(ξ))-expansion technique.This dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrodinger equation.In engineering and applied physics,these wave results have key applications.Graphically,the structures of some solutions are presented by giving specific values to parameters.By using modulation instability analysis,the stability of the model is tested,which shows that the model is stable and the solutions are exact.These techniques can be fruitfully employed to further sculpt models that arise in mathematical physics. 展开更多
关键词 extended F-expansion method generalized exp(-φ(ξ))-expansion technique perturbed Kaup-Newell Schr?dinger equation traveling wave solutions
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TWO TYPES OF TRAVELING WAVE SOLUTIONS TO BURGERS-KdV EQUATIONS
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作者 张玉峰 张鸿庆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第10期1119-1122,共4页
Two types of exact traveling wave solutions to Burgers-KdV equation by basis on work of XIONG Shu-lin are presented. Furthermore, same new results are replenished in work of FAN En-gui et al.
关键词 Burgers-KdV equation traveling wave solution Riccati equation
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Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation
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作者 Zhen-Shu Wen Li-Juan Shi 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第9期162-165,共4页
We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions... We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the threedimensional parameter space. Then we show the required conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like(antikink-like) wave solutions, and compactons. Moreover, we present exact expressions and simulations of these traveling wave solutions. The dynamical behaviors of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of nonlinear waves. 展开更多
关键词 dynamical behaviors traveling wave solutions Fujimoto-Watanabe equation bifurcations
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Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion
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作者 WANG Zhi-ping XU Rui ZHANG Shi-hua 《Chinese Quarterly Journal of Mathematics》 2015年第2期287-299,共13页
An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower sol... An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state. 展开更多
关键词 VACCINATION traveling wave solution nonlocal diffusion upper-lower solutions
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