Related Experiment Video
Updated: Jun 14, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Regularity and wave study of an advection-diffusion-reaction equation
Ali Akgül1,2, Nauman Ahmed3,4, Muhammad Shahzad3
1Department of Mathematics, Art and Science Faculty, Siirt University, 56100, Siirt, Turkey. aliakgul00727@gmail.com.
Abstract:
In this paper, we investigate the optimal conditions to the boundaries where the unique existence of the solutions to an advection-diffusion-reaction equation is secured by applying the contraction mapping theorem from the study of fixed points. Also, we extract, traveling wave solutions of the underlying equation. To this purpose, a new extended direct algebraic method with traveling wave transformation has been used. Achieved soliton solutions are different functions which are hyperbolic, trigonometric, exponential, and some mixed trigonometric functions. These functions show the nature of solitons. Two and three-dimensional plots are drawn using different values of parameters and coefficients for the comparison and behavior of solitons as combined bright-dark, dark, and bright solitons.
Related Concept Videos
Velocity and Acceleration of a Wave
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time....
Navier–Stokes Equations
Reynolds Transport Theorem
Typical Model Studies
The Integrated Rate Law: The Dependence of Concentration on Time
Temperature Dependence on Reaction Rate
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...

