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Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations
Dissertation (MSc)--University of Pretoria, 2022.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2023
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| _version_ | 1867613451267866624 |
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| access_status_str | Open Access |
| author2 | Banasiak, Jacek |
| author_browse | Banasiak, Jacek |
| author_facet | Banasiak, Jacek |
| collection | Thesis |
| dc_rights_str_mv | © 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2022. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/88914 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:21.406Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/88914 Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations Banasiak, Jacek kkhhaannyy@gmail.com Maqele, Khanyisani UCTD Polynomial nonlinearites Travelling wave solutions Evolution equations Galilean transformation Tanh-method G0/G-method Maple program Dissertation (MSc)--University of Pretoria, 2022. In this work, we focus on a general procedure for finding exact travelling wave solutions for evolution equations with polynomial nonlinearites. Mathematically, looking for travelling wave solutions is asking the question whether a given PDE has solutions invariant under a Galilean transformation; in such a case, it can be reduced to an ODE. We discuss the existence of travelling wave solutions by using phase plane analysis. We show that popular methods such as the tanh-method, G0/G-method and many more are special cases of the presented approach. Analytical solutions to several examples of nonlinear equations are illustrated. In the application, we use the Maple program to compute solutions to nonlinear systems of equations. Mathematics and Applied Mathematics MSc Unrestricted 2023-01-20T09:34:05Z 2023-01-20T09:34:05Z 2023-04-30 2022 Dissertation * A2023 https://repository.up.ac.za/handle/2263/88914 en © 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Polynomial nonlinearites Travelling wave solutions Evolution equations Galilean transformation Tanh-method G0/G-method Maple program Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations |
| title | Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations |
| title_full | Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations |
| title_fullStr | Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations |
| title_full_unstemmed | Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations |
| title_short | Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations |
| title_sort | beyond the tanh method looking for explicit travelling wave solutions to partial differential equations |
| topic | UCTD Polynomial nonlinearites Travelling wave solutions Evolution equations Galilean transformation Tanh-method G0/G-method Maple program |
| url | https://repository.up.ac.za/handle/2263/88914 |