SNAKING OF SWIFT-HOHENBERG EQUATION WITH VARIATIONS ON NONLINEAR AND SECOND DERIVATIVE COEFFICIENTS

• Main Author: Sarti, Lialy
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/79887
• Institution: Institut Teknologi Bandung

Motivated by fluid dynamics, diffusion chemical reactions, and biological systems, researchers are interested in the pattern formation of nonequilibrium systems in describing processes in nature. Patterns are structural regularities that can be found in nature. In some cases, patterns are a direct result of fluid instability. Over the past few decades, the Rayleigh–B´enard convection instability has become the paradigm of pattern formation studies. One of the most successful theories in explaining the formation of such convection patterns is homoclinic snaking. Then, the standard model for pattern formation and the commonly studied equation for homoclinic snaking is the Swift-Hohenberg equation. Therefore, this thesis will analyze snaking in the Swift-Hohenberg equation with cubic and quintic nonlinearities by varying the nonlinear and the second derivative coefficients. This thesis aims to analyze the effect of variations of nonlinear coefficient (b3) and second derivative coefficient (a) on uniform, periodic, and snaking solutions. The method used is the pseudo-arclength continuation method. The simulation results show that the variations of the values of b3 and a has a significant influence on the bifurcation point, the stability of the uniform solution, and the system energy (Maxwell point). Furthermore, the snaking behavior of the Swift-Hohenberg equation can be seen from the pinning region. The effect of varying the value of b3 on snaking can be seen from the pinning region which widens as the value of b3 increases. This means that the snaking initially widens but will disappear around the value of b3 = 3.5 due to the influence of energy from the system. Snaking initially forms a snaking pattern but disappears and eventually moves straight up or to a point called the second Maxwell point or ?M2. In contrast to the variation of the value of a where the smaller the value of a, the pinning region widens. This means that the snaking initially widens but disappears around the value of a = 1.2 because there is a second Maxwell point or ?M2.