Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation
In this paper, a (3+1)-dimensional nonlinear evolution equation is considered. First, its bilinear formalism is derived by introducing dependent variable transformation. Then, its breather wave solutions are obtained by employing the extend homoclinic test method and related figures are presented to...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022864?viewType=HTML |
| _version_ | 1811218960521101312 |
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| author | Sixing Tao |
| author_facet | Sixing Tao |
| author_sort | Sixing Tao |
| collection | DOAJ |
| description | In this paper, a (3+1)-dimensional nonlinear evolution equation is considered. First, its bilinear formalism is derived by introducing dependent variable transformation. Then, its breather wave solutions are obtained by employing the extend homoclinic test method and related figures are presented to illustrate the dynamical features of these obtained solutions. Next, its resonant multi-soliton solutions are obtained by using the linear superposition principle. Meanwhile, 3D profiles and contour plots are presented to exhibit the process of wave motion. Finally, M-breather wave solutions such as one-breather, two-breather, three-breather and hybrid solutions between breathers and solitons are constructed by applying the complex conjugate method to multi-soliton solutions. Furthermore, their evolutions are shown graphically by choosing suitable parameters. |
| first_indexed | 2024-04-12T07:18:56Z |
| format | Article |
| id | doaj.art-014cfbc2dd2c45cfb2a3413bbd3afb26 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T07:18:56Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-014cfbc2dd2c45cfb2a3413bbd3afb262022-12-22T03:42:23ZengAIMS PressAIMS Mathematics2473-69882022-06-0179157951581110.3934/math.2022864Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equationSixing Tao0School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, ChinaIn this paper, a (3+1)-dimensional nonlinear evolution equation is considered. First, its bilinear formalism is derived by introducing dependent variable transformation. Then, its breather wave solutions are obtained by employing the extend homoclinic test method and related figures are presented to illustrate the dynamical features of these obtained solutions. Next, its resonant multi-soliton solutions are obtained by using the linear superposition principle. Meanwhile, 3D profiles and contour plots are presented to exhibit the process of wave motion. Finally, M-breather wave solutions such as one-breather, two-breather, three-breather and hybrid solutions between breathers and solitons are constructed by applying the complex conjugate method to multi-soliton solutions. Furthermore, their evolutions are shown graphically by choosing suitable parameters.https://www.aimspress.com/article/doi/10.3934/math.2022864?viewType=HTMLbreather wave solutionsrouge wavesresonant multi-soliton solutionsm-breather solutionshybrid solutions |
| spellingShingle | Sixing Tao Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation AIMS Mathematics breather wave solutions rouge waves resonant multi-soliton solutions m-breather solutions hybrid solutions |
| title | Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation |
| title_full | Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation |
| title_fullStr | Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation |
| title_full_unstemmed | Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation |
| title_short | Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation |
| title_sort | breather wave resonant multi soliton and m breather wave solutions for a 3 1 dimensional nonlinear evolution equation |
| topic | breather wave solutions rouge waves resonant multi-soliton solutions m-breather solutions hybrid solutions |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022864?viewType=HTML |
| work_keys_str_mv | AT sixingtao breatherwaveresonantmultisolitonandmbreatherwavesolutionsfora31dimensionalnonlinearevolutionequation |