Scattering of matter-wave soliton and interference of pulses in Bose-Einstein condensate /
In the first part, we investigate the process of soliton scattering by arbitrary external potential by means of collective coordinates approach and numerical simulation of Gross Pitaevskii Equation. We have used the collective coordinates approach to analyze the dynamics of the width and center of m...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
Kuala Lumpur:
Kulliyyah of Science, International Islamic University Malaysia,
2014
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| Subjects: | |
| Online Access: | Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. |
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| Summary: | In the first part, we investigate the process of soliton scattering by arbitrary external potential by means of collective coordinates approach and numerical simulation of Gross Pitaevskii Equation. We have used the collective coordinates approach to analyze the dynamics of the width and center of mass position of a matter-wave soliton subject to interaction with arbitrary external potential and we have developed a variational approximation for describing this phenomenon. It is shown that approximation of the trial function and external potential only in the interaction of the spatial domain is sufficient for adequate description of the soliton scattering process. We have found good agreement between the numerical solution of the original GPE and the results of variational equations during the scattering of a matter wave soliton on potential barriers, while, we have found qualitative agreement during the scattering of a matter wave soliton on potential wells. The validity of the developed approach is illustrated for the Gaussian and Poschl-Teller potentials. In the second part, we address the phenomena of interaction of two pulses in defocusing nonlinear Schrödinger equation. We use initial conditions in the form of two separated bright pulses with the rectangular shape to analyze the interaction. Defocusing nonlinear Schrödinger equation can be solved by using the Inverse Scattering method, where, we can transform the nonlinear problem into scattering problem. By exact solution of the direct scattering problem associated with the defocusing Nonlinear Schrödinger Equation, we have obtained the expressions for long time behavior of the solution. Obtained results interpreted as a nonlinear interference of two pulses. |
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| Physical Description: | xiii, 68 leaves : ill. ; 30cm. |
| Bibliography: | Includes bibliographical references (leaves 51-54). |