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Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis
Miguel Vivas-Cortez1, Saima Arshed2, Maasoomah Sadaf2
1Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Quito, Ecuador.
Plos One
|February 16, 2023
Summary
This study explores the DNA model
Area of Science:
- Biophysics
- Nonlinear Dynamics
- Mathematical Biology
Background:
- The Peyrard-Bishop model is a key model for DNA dynamics.
- Understanding DNA's mechanical and thermal properties is crucial.
- Nonlinear phenomena play a significant role in DNA function.
Purpose of the Study:
- To investigate the dynamical behavior of the Peyrard-Bishop DNA model.
- To extract exact solutions for the model's governing equations.
- To analyze modulation instability in the DNA model.
Main Methods:
- Application of the Unified Method (UM).
- Construction of solitary wave and soliton solutions.
- Analysis of modulation instability.
- Visualization using 2D and 3D plots.
Main Results:
- The Unified Method successfully yielded polynomial and rational function solutions.
- Solitary wave and soliton solutions were constructed, detailing DNA's dynamical behavior.
- Modulation instability was investigated, providing insights into DNA's stability properties.
- Graphical representations illustrated the physical behavior of the solutions.
Conclusions:
- The Unified Method is effective for solving the Peyrard-Bishop DNA model.
- The obtained solutions offer valuable insights into DNA dynamics and stability.
- This research contributes to the understanding of nonlinear phenomena in biological systems.
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