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traveling wave solutions of a nonlocal dispersal SIRS model with spatio-temporal delay

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International Journal of Biomathematics 2017年第5期10卷 239-261页

作者： Zhaohai Ma Rong Yuan School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China

This paper is mainly concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal SIRS model with nonlocal delayed transmissions. We find that the existence and nonexistence of traveling wave solutions are determined by the critical wave speed c^＊. More specifically, we establish the existence of traveling wave solutions for every wave speed c〉c^＊ and R0 〉 1 by means of upper-lower solutions and Schauder＇s fixed point theorem. Nonexistence of traveling wave solutions is obtained by Laplace transform for any wave speed c ∈ （0, c^＊） and R0 〉 1.

关键词： SIRS epidemic model traveling wave solutions nonlocal dispersal nonlocal delay Laplace transform.

traveling wave solutions for shallow water equations

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Journal of Ocean Engineering and Science 2017年第1期2卷 28-33页

作者： U.M.Abdelsalam Department of Mathematics Faculty of ScienceFayoum UniversityAl FayoumEgypt

An extended homogeneous balance method is suggested in this *** on computerized symbolic computation and the homogeneous balance method,new exact traveling wave solutions of nonlinear partial differential equations(PDEs)are *** shallow-water equations represent a simple yet realistic set of equations typically found in atmospheric or ocean modeling applications,we consider the exact solutions of the nonlinear generalized shallow water equation and the fourth order Boussinesq *** this method,with the aid of Mathematica,many new exact traveling wave solutions are successfully obtained.

关键词： Extended homogeneous balance method Shallow water equation Boussinesq equation traveling wave solutions

traveling wave solutions for a diffusive three-species intraguild predation model

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International Journal of Biomathematics 2018年第2期11卷 147-173页

作者： Jian-Jhong Lin Ting-Hui Yang General Education Center National Taipei University of Technology Taipei 10608 Taiwan Department of Mathematics Tamkang University Tamsui Dist. New Taipei City 25137 Taiwan

The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three-species intraguild predation model which means that one predator can eat its potential resource competitors. The method of upper-lower solution is implemented to show the existence of traveling wave solutions. In order to simplify the construction of an admissible pair of upper lower solution, the scheme of strictly con- tracting rectangle is applied. Finally, the minimal speed c＊ of traveling wave solutions of the model is characterized. If the wave speed is greater than c＊, we show the exis- tence of traveling wave solutions connecting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than c＊, the non-existence of such solutions is also established. Furthermore, to illustrate our theoretical results, some numerical simulations are performed and biological meanings are interpreted.

关键词： Three-species model intraguild predation traveling wave solutions contract-ing rectangle omnivory.

traveling wave solutions IN A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND DELAYS

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International Journal of Biomathematics 2012年第1期5卷 17-33页

作者： YANKE DU RUI XU Institute of Applied MathematicsShijiazhuang Mechanical Engineering College Shijiazhuang 050003P.R.China

This paper deals with the existence of traveling wave solutions in a three-species food-chain model with spatial diffusion and time delays due to gestation and negative feedback. By using a cross iteration scheme and Schauder＇s fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the trivial steady state and the positive steady state. Numerical simulations are carried out to illustrate the main results. In particular, our results extend and improve some known results.

关键词： traveling wave solutions upper-lower solutions partial exponentialquasi-monotonicity Schauder's fixed point theorem food chain.

Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrodinger dynamical model and its applications

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Chinese Physics B 2021年第2期30卷 154-163页

作者： Xiaoyong Qian Dianchen Lu Muhammad Arshad Khurrem Shehzad Faculty of Science Jiangsu UriversityZhenjiang 212013China Department of Mathematics and Statistics University of Agriculture FaisalabadPakistan

We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic *** 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 *** dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrodinger *** engineering and applied physics,these wave results have key ***,the structures of some solutions are presented by giving specific values to *** using modulation instability analysis,the stability of the model is tested,which shows that the model is stable and the solutions are *** techniques can be fruitfully employed to further sculpt models that arise in mathematical physics.

关键词： extended F-expansion method generalized exp(-φ(ξ))-expansion technique perturbed Kaup-Newell Schr?dinger equation traveling wave solutions

Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation

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Chinese Physics B 2018年第9期27卷 162-165页

作者： Zhen-Shu Wen Li-Juan Shi School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China

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.

关键词： dynamical behaviors traveling wave solutions Fujimoto-Watanabe equation bifurcations

A New Integrable (2+1)-Dimensional Generalized Breaking Soliton Equation:N-Soliton solutions and traveling wave solutions

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Communications in Theoretical Physics 2016年第10期65卷 385-388页

作者： Abdul-Majid Wazwaz Department of Mathematics Saint Xavier University

In this work,we study a new(2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of *** derive multiple soliton solutions,traveling wave solutions,and periodic ... 详细信息

关键词： breaking soliton equations Hirota bilinear method multiple soliton solutions traveling wave solutions

Bifurcations and Dynamics of traveling wave solutions to a Fujimoto-Watanabe Equation

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Communications in Theoretical Physics 2018年第6期69卷 631-636页

作者： Li-Juan Shi Zhen-Shu Wen School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China

In this paper, we study the bifurcations and dynamics of traveling wave solutions to a Fujimoto-Watanabe equation by using the method of dynamical systems. We obtain a11 possible bifurcations of phase portraits of the system in different regions of the parametric space. Then we show the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, eompactions and kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions and periodic wave solutions are implicitly given, while the expressions of kink-like and antikink-like wave solutions are explicitly shown. The dynamics 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 the nonlinear wave.

关键词： Fujimoto-Watanabe equation traveling wave solutions bifurcations dynamics

EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF traveling wave solutions

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Chinese Annals of Mathematics,Series B 2001年第3期22卷 343-360页

作者： ZHANG LINGHAI School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN 55455, USA. School of Mathematics University of Minnesota 206 Church Street S. E. Minneapolis MN 55455 USA

This paper studies the asymptotic stability of traveling we solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some "nice structure" of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.

关键词： traveling wave solutions Asymptotic stability Eigenvalue problem Normal spectrum Evans function