SNAKING PHENOMENON ON STUB LATTICE

• Main Author: Sa'di Subhan, Muslihuddin
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/85862
• Institution: Institut Teknologi Bandung

The nonlinear Schr¨odinger equation is an equation that is often applied invarious fields of science, both in continuous and discrete cases. These two cases can produce a snaking phenomenon, with the main factor being in the discrete case is the Laplacian part. This research will examine the phenomenon of snaking on discrete nonlinear Schr¨odinger equation with one-dimensional stub lattice. The linear stability of the uniform solution can be tested using the relation equation dispersion. This equation is obtained by finding a solution around the uniform solution which has a form similar to the solution of the diffusion equation. Analysis of changes in localized solutions to frequency parameters can show snaking behavior. This snaking is seen as a change in the stability of the localized solution produces a snaking bifurcation diagram. The snaking width will decrease along with increasing coupling strength, shows that equation will not have snaking in the continuous case. This snaking width is called as a pinning region. In the case of a one-dimensional stub lattice, the site is divided into three section to simplify definitions. This system has a uniform solution with linear stability similar to the one-dimensional lattice case. Main differences in a one-dimensional stub lattice there are three dispersion relation equations. In the bistable region, there are localized solutions of two types: c-centred and ac-centred. Snaking in the case of one-dimensional stub lattices occurs in both types this solution, because the localized solution obtained has symmetry properties. Snaking will also show an additional case called switchback, namely interaction convoluted caused by non-uniformity of the front due to structural differences. Pinning regions for switchbacks will disappear faster in comparison with the pinning region of the main snaking as the coupling strength increases. Besides, the pinning region in a one-dimensional stub lattice is larger than in a one-dimensional stub lattice dimensions, as the slightly wider stub lattice structure requires couplings higher strength to eliminate snaking cases.