Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation
Fan et al. studied the bifurcations of traveling wave solutions for a two-component Fornberg-Whitham equation. They gave a part of possible phase portraits and obtained some uncertain parametric conditions for solitons and kink (antikink) solutions. However, the exact explicit parametric conditions...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/704931 |
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| author | Zhenshu Wen |
| author_facet | Zhenshu Wen |
| author_sort | Zhenshu Wen |
| collection | DOAJ |
| description | Fan et al. studied the bifurcations of traveling wave solutions for a two-component Fornberg-Whitham equation. They gave a part of possible phase portraits and obtained some uncertain parametric conditions for solitons and kink (antikink) solutions. However, the exact explicit parametric conditions have not been given for the existence of solitons and kink (antikink) solutions. In this paper, we study the bifurcations for the two-component Fornberg-Whitham equation in detalis, present all possible phase portraits, and give the exact explicit parametric conditions for various solutions. In addition, not only solitons and kink (antikink) solutions, but also peakons and periodic cusp waves are obtained. Our results extend the previous study. |
| format | Article |
| id | doaj-art-878c32f4b139445594154433ec4acf58 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-878c32f4b139445594154433ec4acf582025-02-03T05:59:34ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/704931704931Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham EquationZhenshu Wen0School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaFan et al. studied the bifurcations of traveling wave solutions for a two-component Fornberg-Whitham equation. They gave a part of possible phase portraits and obtained some uncertain parametric conditions for solitons and kink (antikink) solutions. However, the exact explicit parametric conditions have not been given for the existence of solitons and kink (antikink) solutions. In this paper, we study the bifurcations for the two-component Fornberg-Whitham equation in detalis, present all possible phase portraits, and give the exact explicit parametric conditions for various solutions. In addition, not only solitons and kink (antikink) solutions, but also peakons and periodic cusp waves are obtained. Our results extend the previous study.http://dx.doi.org/10.1155/2012/704931 |
| spellingShingle | Zhenshu Wen Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation Abstract and Applied Analysis |
| title | Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation |
| title_full | Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation |
| title_fullStr | Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation |
| title_full_unstemmed | Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation |
| title_short | Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation |
| title_sort | extension on bifurcations of traveling wave solutions for a two component fornberg whitham equation |
| url | http://dx.doi.org/10.1155/2012/704931 |
| work_keys_str_mv | AT zhenshuwen extensiononbifurcationsoftravelingwavesolutionsforatwocomponentfornbergwhithamequation |