Traveling wave solutions to modified Burgers and diffusionless Fisher PDE's

Ronald Mickens; Kale Oyedeji

doi:10.3934/eect.2019008

Article Contents

2019, Volume 8, Issue 1: 139-147. Doi: 10.3934/eect.2019008

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Traveling wave solutions to modified Burgers and diffusionless Fisher PDE's

Ronald Mickens^1, and
Kale Oyedeji^2, ,

1.
Clark Atlanta University, Department of Physics, Atlanta, GA 30314, USA
2.
Morehouse College, Department of Physics, Atlanta, GA 30314, USA

Corresponding author: Kale Oyedeji, 470-639-0285
Corresponding author: Kale Oyedeji, 470-639-0285

Received: October 2017

Revised: January 2018

Early access: December 2018

Published: January 2019

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Abstract

We investigate traveling wave (TW) solutions to modified versionsof the Burgers and Fisher PDE’s. Both equations are nonlinear parabolicPDE’s having square-root dynamics in their advection and reaction terms.Under certain assumptions, exact forms are constructed for the TW solutions.

Keywords:

Mathematics Subject Classification: Primary: 34E05, 35K57; Secondary: 35B09, 35B40.

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Figure 1. a) $ v(z) $ vs $ z $, b) $ f(z) = v(z)^2 $ vs $ z $. See Eqs. (5.10) and (5.13).

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Figure 2. a) $ v(z) $ vs $ z $, \quad b) $ f(z) $ vs $ z $. See Eq. (5.15).

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