Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

Area of Science:

• Chemical kinetics
• Mathematical modeling
• Reaction-diffusion systems

Background:

• The Lengyel-Epstein system models chemical reactions with spatial diffusion.
• Understanding wave propagation in such systems is crucial for various scientific fields.
• Analytical solutions for complex reaction-diffusion models are often challenging to obtain.

Purpose of the Study:

• To analytically investigate the Lengyel-Epstein reaction-diffusion system.
• To explore abundant families of solitary wave structures within this system.
• To derive exact solitary wave solutions and analyze their properties.

Main Methods:

• Application of the generalized Riccati equation mapping method.
• Analytical derivation of exact solitary wave solutions.
• Numerical visualization using 3D and contour plots to illustrate physical behavior.

Main Results:

• Identification of diverse solitary wave structures, including shock, complex solitary-shock, shock singular, and periodic-singular forms.
• Emergence of rational solutions during the derivation process.
• Demonstration that solitary wave propagation speed is influenced by the interplay of diffusive and reactive effects and reaction kinetics.

Conclusions:

• The generalized Riccati equation mapping method successfully yields exact solitary wave solutions for the Lengyel-Epstein system.
• The system exhibits a rich variety of wave phenomena, offering insights into pattern formation.
• The study provides a comprehensive analytical framework for understanding complex wave dynamics in reaction-diffusion systems.