Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species

Nonlinearity ◽  
2020 ◽  
Vol 33 (10) ◽  
pp. 5080-5110 ◽  
Author(s):  
Chueh-Hsin Chang ◽  
Chiun-Chuan Chen ◽  
Li-Chang Hung ◽  
Masayasu Mimura ◽  
Toshiyuki Ogawa
Keyword(s):  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Volterra System ◽  
Competing Species ◽  
Wave Solutions ◽  
Existence And Stability

Existence and stability of travelling wave solutions for an evolutionary ecology model

1990 ◽  
Vol 115 (1-2) ◽  
pp. 1-18 ◽  
Author(s):  
Roger Lui
Keyword(s):  
Population Size ◽  
Evolutionary Ecology ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Fisher’S Equation ◽  
Wave Solutions ◽  
Fisher's Equation ◽  
Existence And Stability ◽  
The Stability

SynopsisMonotone travelling wave solutions are known to exist for Fisher's equation which models the propagation of an advantageous gene in a single locus, two alleles population genetics model. Fisher's equation assumed that the population size is a constant and that the fitnesses of the individuals in the population depend only on their genotypes. In this paper, we relax these assumptions and allow the fitnesses to depend also on the population size. Under certain assumptions, we prove that in the second heterozygote intermediate case, there exists a constant θ*>0 such that monotone travelling wave solutions for the reaction–diffusion system exist whenever θ > θ*. We also discuss the stability properties of these waves.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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