ANALYSIS OF SNAKING SOLUTIONS IN THE SWIFT-HOHENBERG EQUATION WITH VARIATION OF THE FOURTH-ORDER DERIVATIVE COEFFICIENT

• Main Author: NOVALINDA, AMIRA
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/79881
• Institution: Institut Teknologi Bandung

Mathematical modeling plays a crucial role in unraveling natural phenomena, particularly pattern formation in materials. This research focuses on the Swift- Hohenberg equation with cubic-quintic nonlinear terms, considered a relevant model for describing the complex dynamics of pattern formation. The study explores the influence of varying cubic-quintic nonlinear and fourth-order derivative coefficients on the properties of uniform, periodic, and localized solutions. The problem statement encompasses inquiries into the characteristics of solutions and the snaking phenomenon within the context of the Swift-Hohenberg equation. The research aims to delve into these aspects, analyze the impact of parameters on pattern formation, and understand system bifurcations. The conclusions of this study detail comprehensive analyses of uniform, periodic, and snaking solutions in the Swift-Hohenberg equation. Variant parameters reveal intricate bifurcation diagrams and complex dynamics. The research provides profound insights into the nature of pattern formation in materials. This study makes a significant contribution to our understanding of nonlinear system dynamics, especially in the context of pattern formation. Suggestions for future research include further exploration of additional parameters and experimental validation to test the model’s applicability in more specific natural phenomena contexts.