Numerical Investigations Of The Complex Swift-Hohenberg Equation

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dc.contributor.authorKhairudin, Nur Izzati
dc.date.accessioned2018-01-24T07:45:15Z
dc.date.available2018-01-24T07:45:15Z
dc.date.issued2017-08
dc.description.abstractComplex Swift-Hohenberg equation (CSHE) is a model used to study various aspects of pattern formation in applied mathematics and mathematical physics. Essentially, the CSHE can be considered as generalization of the nonlinear Schrödinger equation, an equation that exhibit solitary wave solution. It is known that solitary wave solutions were used to detect physical phenomena such as the tsunami wave. In this research, investigation on some of the properties of the CSHE and its solutions were conducted. This research is divided into three parts. Firstly, the stability of fixed points of the CSHE using a modified variational formulation was analyzed. In the second part, investigation on an approximate soliton solution to the CSHE using the cosine function method was discussed. The final part discussed the stability of the fixed points for two cases of the dispersionless CSHE, namely for the dispersion-free and for the destabilized dispersion. The modified variational formulation was reused in the third part. From the first part, the system exhibit a focus and stationary soliton. Due to the stability of Jacobian eigenvalues, the fixed points of the CSHE were stable. The findings from the first part have shown that no bifurcation existed in the transition from fixed points to limit cycle in the system. The contribution occurred in the second part where an analytical solution to the CSHE was obtained. The existence of frequency in the system was established due to the nonlinear gain in the CSHE. The findings from the second part have shown that the propagation of plain stationary pulses was obtained in the system while varying the values of nonlinear gain and frequency. In the third part, the system depended on nonlinearity, since the dispersion essentially has no effect on the system. It was found that the fixed points of dispersionless CSHE were stable when the system evaluated at the nonlinear gain and linear loss. Stationary and exploding solitons have been found under this problem. From the findings, the properties of the CSHE and its solutions can be extended to understand several other pattern formations in both cavity solitons and spatiotemporal dissipative solitons.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/5457
dc.language.isoenen_US
dc.publisherUniversiti Sains Malaysiaen_US
dc.subjectComplex Swift-Hohenberg equation is a model used to studyen_US
dc.subjectvarious aspects of pattern formation in applied mathematics.en_US
dc.titleNumerical Investigations Of The Complex Swift-Hohenberg Equationen_US
dc.typeThesisen_US
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