M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water
Abstract In this paper, we use the Hirota bilinear method for investigating the third-order evolution equation to determining the soliton-type solutions. The M lump solutions along with different types of graphs including contour, density, and three- and two-dimensional plots have been made. Moreove...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02669-y |
| _version_ | 1819228599578787840 |
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| author | Onur Alp Ilhan Jalil Manafian As’ad Alizadeh Sizar Abid Mohammed |
| author_facet | Onur Alp Ilhan Jalil Manafian As’ad Alizadeh Sizar Abid Mohammed |
| author_sort | Onur Alp Ilhan |
| collection | DOAJ |
| description | Abstract In this paper, we use the Hirota bilinear method for investigating the third-order evolution equation to determining the soliton-type solutions. The M lump solutions along with different types of graphs including contour, density, and three- and two-dimensional plots have been made. Moreover, the interaction between 1-lump and two stripe solutions and the interaction between 2-lump and one stripe solutions with finding more general rational exact soliton wave solutions of the third-order evaluation equation are obtained. We give the theorem along with the proof for the considered problem. The existence criteria of these solitons in the unidirectional propagation of long waves over shallow water are also demonstrated. Various arbitrary constants obtained in the solutions help us to discuss the graphical behavior of solutions and also grants flexibility in formulating solutions that can be linked with a large variety of physical phenomena. We further show that the assigned method is general, efficient, straightforward, and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering. We have depicted the figures of the evaluated solutions to interpret the physical phenomena. |
| first_indexed | 2024-12-23T10:59:51Z |
| format | Article |
| id | doaj.art-b12e8b2297fe4279b20acdd1fed0a007 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T10:59:51Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-b12e8b2297fe4279b20acdd1fed0a0072022-12-21T17:49:40ZengSpringerOpenAdvances in Difference Equations1687-18472020-05-012020112010.1186/s13662-020-02669-yM lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow waterOnur Alp Ilhan0Jalil Manafian1As’ad Alizadeh2Sizar Abid Mohammed3Department of Mathematics, Faculty of Education, Erciyes UniversityDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of TabrizDepartment of Mechanical Engineering, Urmia University of TechnologyDepartment of Mathematics, College of Basic Education, University of DuhokAbstract In this paper, we use the Hirota bilinear method for investigating the third-order evolution equation to determining the soliton-type solutions. The M lump solutions along with different types of graphs including contour, density, and three- and two-dimensional plots have been made. Moreover, the interaction between 1-lump and two stripe solutions and the interaction between 2-lump and one stripe solutions with finding more general rational exact soliton wave solutions of the third-order evaluation equation are obtained. We give the theorem along with the proof for the considered problem. The existence criteria of these solitons in the unidirectional propagation of long waves over shallow water are also demonstrated. Various arbitrary constants obtained in the solutions help us to discuss the graphical behavior of solutions and also grants flexibility in formulating solutions that can be linked with a large variety of physical phenomena. We further show that the assigned method is general, efficient, straightforward, and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering. We have depicted the figures of the evaluated solutions to interpret the physical phenomena.http://link.springer.com/article/10.1186/s13662-020-02669-yHirota bilinear methodThird-order evolution equationM-lump solutionsInteractionThe unidirectional propagationThe existence criteria |
| spellingShingle | Onur Alp Ilhan Jalil Manafian As’ad Alizadeh Sizar Abid Mohammed M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water Advances in Difference Equations Hirota bilinear method Third-order evolution equation M-lump solutions Interaction The unidirectional propagation The existence criteria |
| title | M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water |
| title_full | M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water |
| title_fullStr | M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water |
| title_full_unstemmed | M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water |
| title_short | M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water |
| title_sort | m lump and interaction between m lump and n stripe for the third order evolution equation arising in the shallow water |
| topic | Hirota bilinear method Third-order evolution equation M-lump solutions Interaction The unidirectional propagation The existence criteria |
| url | http://link.springer.com/article/10.1186/s13662-020-02669-y |
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