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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.
Scientific Reports
|September 5, 2024
Summary
This study identifies optimal boundary conditions for advection-diffusion-reaction equations using the contraction mapping theorem. It also extracts diverse traveling wave and soliton solutions, revealing their behavior through visualizations.
Area of Science:
- Mathematical Physics
- Nonlinear Partial Differential Equations
Background:
- Advection-diffusion-reaction equations model complex phenomena.
- Ensuring unique solutions requires understanding boundary conditions.
- Traveling wave solutions are crucial for analyzing wave propagation.
Purpose of the Study:
- To determine optimal boundary conditions for the unique existence of solutions.
- To extract traveling wave solutions for the advection-diffusion-reaction equation.
- To analyze the behavior of various soliton solutions.
Main Methods:
- Application of the contraction mapping theorem (fixed-point theory).
- Utilizing a new extended direct algebraic method.
- Employing traveling wave transformations.
Main Results:
- Established conditions for the unique existence of solutions.
- Derived diverse soliton solutions including hyperbolic, trigonometric, and exponential forms.
- Visualized soliton behaviors (bright-dark, dark, bright) using 2D and 3D plots.
Conclusions:
- The contraction mapping theorem effectively secures unique solutions.
- The extended algebraic method successfully extracts a variety of soliton solutions.
- Parameter variations significantly influence soliton characteristics.
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