Traveling Wave Solution of a Reaction–Diffusion Predator–Prey System

Liu, Jiang; Xu, Dongcheng; Du, Zhijiang

doi:10.1007/s12346-018-0276-1

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…This model can be reduced to other models, like the Landau-Ginzburg-Higgs, Klein-Gordon, and sine-Gordon equations. According to the various application fields of nonlinear partial differential equations, many methods have been discovered and derived to study the exact and approximate solutions; for more details about some of these methods, see References [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In this research, we applied twelve methods to our nonlinear fractional unforced Duffing equation to study the properties of solutions and also the convergence among our solutions.…”

Section: Introductionmentioning

confidence: 99%

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Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

Attia

Khater

2019

MCA

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This paper studies the nonlinear fractional undamped Duffing equation. The Duffing equation is one of the fundamental equations in engineering. The geographical areas of this model represent chaos, relativistic energy-momentum, electrodynamics, and electromagnetic interactions. These properties have many benefits in different science fields. The equation depicts the energy of a point mass, which is well thought out as a periodically-forced oscillator. We employed twelve different techniques to the nonlinear fractional Duffing equation to find explicit solutions and approximate solutions. The stability of the solutions was also examined to show the ability of our obtained solutions in the application. The main goals here were to apply a novel computational method (modified auxiliary equation method) and compare the novel method with other methods via the solutions that were obtained by each of these methods.

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Section: Introductionmentioning

confidence: 99%

“…Equations (11), (13), (22), (29), (35), (37), (40), and (91) are convergent to each other by equating the parameters in each solution.…”

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confidence: 99%

Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

Attia

Khater

2019

MCA

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Existence of Solitary Wave Solutions for a Nonlinear Fifth-Order KdV Equation

Liu

2020

Qual. Theory Dyn. Syst.

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Traveling wave solutions of a diffusive predator-prey system with Holling II type functional response

Liu¹,

Wu²,

Lin³

et al. 2024

Proc. Amer. Math. Soc.

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In this paper, we discuss a three-dimensional diffusive predator-prey system with nonlocal terms and Holling II type functional response. According to the relationship between traveling wave and heteroclinic orbit, the predator-prey system is transformed into the singularly perturbed system. Based on the method of the geometric singular perturbation theory, we construct a locally invariant manifold to obtain the traveling wave solutions with nonlocal delay convolution kernel.

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Traveling Wave Solution of a Reaction–Diffusion Predator–Prey System

Cited by 3 publications

References 22 publications

Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

Existence of Solitary Wave Solutions for a Nonlinear Fifth-Order KdV Equation

Traveling wave solutions of a diffusive predator-prey system with Holling II type functional response

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