NON-LINEAR SCHRÃDINGER ANALYSIS WITH FRACTIONAL LAPLACIAN FACTOR
This research study the dynamics of Non-Linear Schrödinger Equation using the fractional factor, (?)?/2. It studied about the dynamics, stability, and the bifurcation diagram of equation with bifurcation points ?. Non-Linear Schrödinger Equation is one of the equation that represent habits of Bos...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/81265 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This research study the dynamics of Non-Linear Schrödinger Equation using the fractional
factor, (?)?/2. It studied about the dynamics, stability, and the bifurcation diagram
of equation with bifurcation points ?. Non-Linear Schrödinger Equation is one of the
equation that represent habits of Bose-Einstein Condensate in a trap, called V (x). In this
study, V (x) or the potentials is a parabolic trap, that is x2. There are several methods to
analyze the equation, such as : Fourier Transform and FDMx to construct a fractional
differentiation matrix operator, runge-kutta 4 to solve the Differential Equation for time
dynamics, and numerical method of root finding to analyze the stability of the solution.
This equation analyzed gradually, started from solution in real field, complex field with
zero potentials, complex field with parabolic trap, and complex field with parabolic trap
and fractional laplacian factor. At the end of this paper, it found that the solution of
fractional Non-Linear Schrödinger Equation tends unstable along the reduction of ?. |
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