scholarly journals Theory of fads: Traveling-wave solution of evolutionary dynamics in a one-dimensional trait space

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
Mi Jin Lee ◽  
Su Do Yi ◽  
Beom Jun Kim ◽  
Seung Ki Baek
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Evolutionary Dynamics ◽  
Traveling Wave Solution ◽  
One Dimensional ◽  
Trait Space

scholarly journals Traveling wave solutions for a class of reaction-diffusion system

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bingyi Wang ◽  
Yang Zhang
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
One Dimensional ◽  
Wave Solutions

AbstractIn this paper we investigate the existence of traveling wave for a one-dimensional reaction diffusion system. We show that this system has a unique translation traveling wave solution.

scholarly journals SOME PROPERTIES OF FRACTIONAL BURGERS EQUATION

2002 ◽  
Vol 7 (1) ◽  
pp. 151-158 ◽  
Author(s):  
P. Miškinis
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Conservation Laws ◽  
Traveling Wave ◽  
Wave Solution ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Traveling Wave Solution ◽  
One Dimensional ◽  
Liouville Fractional Derivative

The fractional generalization of a one‐dimensional Burgers equationwith initial conditions ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), where ɸ = ɸ(x,t) ∈ C2(Ω): ɸt = δɸ/δt; aDx p is the Riemann‐Liouville fractional derivative of the order p; Ω = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf‐Cole transformation are discussed.

scholarly journals ON A MACROSCOPIC LIMIT OF A KINETIC MODEL OF ALIGNMENT

2013 ◽  
Vol 23 (14) ◽  
pp. 2647-2670 ◽  
Author(s):  
JACEK BANASIAK ◽  
MIROSŁAW LACHOWICZ
Keyword(s):  
Kinetic Model ◽  
Diffusion Equation ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Navier Stokes ◽  
Order Of Approximation ◽  
Linear Diffusion ◽  
One Dimensional ◽  
Position And Orientation

In the present paper we study the macroscopic limits of a kinetic model for interacting entities (individuals, organisms, cells). The kinetic model is one-dimensional and the entities are characterized by their position and orientation (+/-) with swarming interaction controlled by a sensitivity parameter. The macroscopic limits of the model are considered for solutions close either to the diffusive (isotropic) or to the aligned (swarming) equilibrium states for various values of that parameter. In the former case the classical linear diffusion equation results whereas in the latter a traveling wave solution does both in the zeroth ("Euler") and first ("Navier–Stokes") order of approximation.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Periodic traveling-wave solution of the Sakuma-Nishiguchi equation

1996 ◽  
Vol 54 (19) ◽  
pp. 13484-13486 ◽  
Author(s):  
David R. Rowland ◽  
Zlatko Jovanoski
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Periodic Traveling Wave

scholarly journals Stability Analysis of an Age-Structured SEIRS Model with Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 455 ◽  
Author(s):  
Zhe Yin ◽  
Yongguang Yu ◽  
Zhenzhen Lu
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Traveling Wave ◽  
Wave Solution ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Traveling Wave Solution ◽  
Age Structured ◽  
Nonlinear Autonomous System ◽  
Disease Free

This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.

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