Rani, Mehwish (2023) Exact Solitary Wave Solutions of Some Non-Linear Partial Differential Equations arising in Wave Propagation and Optical Fibers. PhD thesis, Victoria University.

Abstract

One of the most intriguing areas of applied mathematics is the study of non-linear partial differential equations (NLPDEs). They play a pivotal role in describing, modelling, and predicting many real-life phenomena. Due to the abstract nature, the fundamental problem is to find their exact solutions. Several methods have been proposed for this purpose. The study aims to find out unexplored exact solitary wave solutions to some NLPDEs arising in the fields of wave propagation and optical fiber. We shall be dealing with nonlinear dispersive PDEs. They are the ones where we could expect to have special type of exact solutions known as solitary wave solutions or solitons. Since solitons have been proven to be the exact solutions of many families of NLPDEs, their complete understanding would lead us to a broad understanding of the real-life phenomena themselves. In this thesis, modified extended tanh method, improved tanh expansion method, generalized auxiliary equation mapping method, and improved generalized Riccati equation method have been used to solve few distinguished NLPDEs and NLFPDEs. The results obtained by these methods are new and have not been reported in literature previously proves the efficacy and productiveness of these methods. The main objective of this research is to find new exact solutions and graphical visualization of these results of PDE of integer and fractional order. This project has two aspects of its significance. One is purely mathematical, and the other is its applications in other fields of science and technology. The new solutions would help scientists in developing cost-effective simulators to understand complex qualitative features of many phenomena in the fields of wave-propagation and signal-processing.

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